Paper Citation Record · LEDGER

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow

As of 8 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.04937.

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pith.paper-citation-record.v1
2506.04937 v1

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measured 35 of 35 reference resolution

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measured 35 of 35 standing notices

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Outbound references

Observation 3fe9149f-084c-42ed-806d-ccdf4b9f7438 · outbound

This paper cites Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.551956Z

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Observation b57afc3e-7e0b-453f-a55d-e09e00fc1fe7 · outbound

This paper cites Gradient estimates for the heat equation under the Ricci-harmonic map flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Gradient estimates for the heat equation under the Ricci-harmonic map flow

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.538415Z

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Observation 61cdf08a-def5-4194-802d-9b1749c143ea · outbound

This paper cites Gradient estimates for the heat equation under the Ricci flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Gradient estimates for the heat equation under the Ricci flow

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.521208Z

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Observation 86792135-f5b8-4e73-9668-ff26c66911c2 · outbound

This paper cites Parabolic frequency on Ricci flows.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Parabolic frequency on Ricci flows

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.503473Z

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Observation 165541cd-17e5-4106-951d-44ee0ca015ad · outbound

This paper cites Parabolic frequency for the mean curvature flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Parabolic frequency for the mean curvature flow

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.487614Z

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Observation a94719c4-da28-45d7-85e1-774a3c2a14aa · outbound

This paper cites Lu, and L.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Lu, and L

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.473070Z

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Observation c02a947d-68d0-4de4-94a7-b684e1b3afa7 · outbound

This paper cites Harmonic functions with polynomial growth.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Harmonic functions with polynomial growth

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.457278Z

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Observation 34edf084-d5b4-4f0a-a18f-a1da8b3b74e5 · outbound

This paper cites Parabolic frequency on manifolds.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Parabolic frequency on manifolds

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.442483Z

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Observation 6fae6501-64b0-4259-b431-4501d7eb89ca · outbound

This paper cites Ricci flow, Killing spinors, and T-duality in generalized geometry.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Ricci flow, Killing spinors, and T-duality in generalized geometry

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.426434Z

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Observation 4dda47b2-09a1-44c0-b25a-09688e8ffbd8 · outbound

This paper cites Streets.Generalized Ricci flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Streets.Generalized Ricci flow

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.412943Z

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Observation f6616e36-979e-4dc8-bb40-9609fc0a2af0 · outbound

This paper cites Monotonicity properties of variational integrals,A p weights and unique continuation.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Monotonicity properties of variational integrals,A p weights and unique continuation

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.397497Z

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Observation 7c79f139-bdef-4f6a-8030-da4573c85e92 · outbound

This paper cites Unique continuation for elliptic operators: a geometric- variational approach.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Unique continuation for elliptic operators: a geometric- variational approach

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.384592Z

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Observation 3803d451-efe2-4050-9a23-484239c5ab0c · outbound

This paper cites A matrix Harnack estimate for the heat equation.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow A matrix Harnack estimate for the heat equation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.369538Z

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Observation f19b3053-39b0-4fdc-89b8-16cde4c7caea · outbound

This paper cites Geometric measure of singular sets of elliptic equations.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Geometric measure of singular sets of elliptic equations

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.354107Z

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Observation a6dfdc96-4daa-4947-a2b9-117710c44f71 · outbound

This paper cites On the shrinking entropy functional for generalized Ricci flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow On the shrinking entropy functional for generalized Ricci flow

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.341442Z

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Observation 7528c1d2-bc22-43b9-8552-c5b53c117417 · outbound

This paper cites Geometric measure of singular sets of elliptic equations.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Geometric measure of singular sets of elliptic equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.328877Z

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Observation e8222dec-dab6-413d-8945-a74e200ec514 · outbound

This paper cites Parabolic frequency monotonicity on Ricci flow and Ricci- harmonic flow with bounded curvatures.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Parabolic frequency monotonicity on Ricci flow and Ricci- harmonic flow with bounded curvatures

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.318673Z

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Observation f6587948-15ec-4e26-9550-94061a48dd02 · outbound

This paper cites Gradient estimates and parabolic frequency under the LaplacianG 2 flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Gradient estimates and parabolic frequency under the LaplacianG 2 flow

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.307802Z

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Observation 976e5e2c-b0d2-4c57-8111-241484b4fe9c · outbound

This paper cites On the parabolic kernel of the Schr¨ odinger operator.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow On the parabolic kernel of the Schr¨ odinger operator

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.297110Z

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Observation 8042c5dc-73f3-499c-a656-f32493ce04ec · outbound

This paper cites Parabolic frequency monotonicity on compact manifolds.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Parabolic frequency monotonicity on compact manifolds

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.286586Z

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Observation d9922dc4-9e4a-4a43-ae65-40834d6d5e5a · outbound

This paper cites Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.275986Z

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Observation 013c66fd-e272-4a5f-afbe-bb8c64087d81 · outbound

This paper cites Entropy and heat kernel on generalized Ricci flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Entropy and heat kernel on generalized Ricci flow

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.265602Z

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Observation a265a1db-2f91-4e1a-9044-95e0d2a8e671 · outbound

This paper cites Nodal sets of solutions of elliptic and parabolic equations.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Nodal sets of solutions of elliptic and parabolic equations

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.254400Z

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Observation 08eea182-cd20-4253-9e7c-b6683149798d · outbound

This paper cites A note on parabolic frequency and a theorem of Hardy-P´ olya-Szeg¨ o.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow A note on parabolic frequency and a theorem of Hardy-P´ olya-Szeg¨ o

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.243818Z

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Observation 3dce8e63-6149-4549-bf8a-3e304f1ca170 · outbound

This paper cites Gradient estimates for solutions of the heat equation under Ricci flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Gradient estimates for solutions of the heat equation under Ricci flow

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.232141Z

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Observation 34a048ff-44ae-42d3-8152-094c0ea904b2 · outbound

This paper cites A Harnack inequality for parabolic differential equations.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow A Harnack inequality for parabolic differential equations

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.221937Z

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Observation f349aee7-a91f-4214-b654-d70ff062ac99 · outbound

This paper cites In: Analysis, complexgeometry, and mathematical physics: in honor of Duong H.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow In: Analysis, complexgeometry, and mathematical physics: in honor of Duong H

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.211507Z

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Observation 67eb3fc4-3761-4da2-94af-f5b85b04b772 · outbound

This paper cites A gradient flow for worldsheet nonlinear sigma models.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow A gradient flow for worldsheet nonlinear sigma models

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.201174Z

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Observation 59cca460-7402-4fdc-b9b3-fdc544bebf1b · outbound

This paper cites Unique continuation for parabolic equations.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Unique continuation for parabolic equations

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.191241Z

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Observation 87611d5d-41d8-44d3-b615-5ebced6b7f0a · outbound

This paper cites Generalized geometry, T-duality, and renormalization group flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Generalized geometry, T-duality, and renormalization group flow

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.180741Z

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Observation e0b60fc2-d3ae-4fa0-b9ff-4bc70a907906 · outbound

This paper cites Scalar curvature, entropy, and generalized Ricci flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Scalar curvature, entropy, and generalized Ricci flow

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.168422Z

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Observation 4a97b0e9-f6df-4bf2-b6f2-65b0c25b862e · outbound

This paper cites A parabolic flow of pluriclosed metrics.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow A parabolic flow of pluriclosed metrics

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.157508Z

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Observation 619f21b4-252b-485f-9e5d-3cda21bc5b6a · outbound

This paper cites Generalized K¨ ahler geometry and the pluriclosed flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Generalized K¨ ahler geometry and the pluriclosed flow

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.146098Z

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Observation c5a7bc90-dc14-4da8-8ea7-64bde9b4ad51 · outbound

This paper cites Regularity results for pluriclosed flow.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Regularity results for pluriclosed flow

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.135583Z

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Observation c3ec6f29-24f8-46b9-821b-da5e4111c293 · outbound

This paper cites Some gradient estimates for the heat equation on domains and for an equation by Perelman.

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Some gradient estimates for the heat equation on domains and for an equation by Perelman

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:46:08.124374Z

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