Pith Number

pith:DCOFXIVO

pith:2026:DCOFXIVOE2QEZR2N6NN2LQIHBU

not attested not anchored not stored refs resolved

The inverse curve shortening flow on the hyperbolic plane

Ivan Krznari\'c, Rafael L\'opez

In the hyperbolic plane, all parabolic solitons of the inverse curve shortening flow are graphs over the y-axis and all conformal solitons are graphs over the x-axis in the upper half-plane model.

arxiv:2605.14385 v1 · 2026-05-14 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DCOFXIVOE2QEZR2N6NN2LQIHBU}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We classify all solitons with respect to parabolic and conformal vector fields of H^2. In the upper half-plane model of H^2, we prove that parabolic solitons are all graphs on the y-axis, whereas conformal solitons are graphs on the x-axis.

C2weakest assumption

The flow is assumed to be well-defined for the curves considered, and the vector fields are taken to be parabolic or conformal without further justification of why these are the only relevant cases for soliton classification.

C3one line summary

Solitons for the inverse curve shortening flow on H^2 are classified as graphs over the coordinate axes in the upper half-plane model, with analysis of their concavity and asymptotic behavior.

References

22 extracted · 22 resolved · 0 Pith anchors

[1] B. D. Allen, Non-compact solutions to inverse mean curvature flow in hyperbolic space. Ph.D. thesis, University of Tennessee, Knoxville, 2016 2016

[2] A. Bueno, R. L´ opez, Horo-shrinkers in the hyperbolic space. Taiwanese J. Math. 29 (2025), 1037–1059 2025

[3] A. Bueno, R. L´ opez, The class of grim reapers inH 2 ×R. J. Math. Anal. Appl. 541 (2025), 128730 2025

[4] I. Castro, A. M. Lerma, Lagrangian homothetic solitons for the inverse mean curvature flow. Results Math. 71 (2017), 3–4 2017

[5] B. Choi, P. Daskalopoulos, Evolution of non-compact hypersurfaces by inverse mean curvature. Duke Math. J. 170 (2021), 2755–2803 2021

Receipt and verification

First computed	2026-05-17T23:39:07.677978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

189c5ba2ae26a04cc74df35ba5c1070d248b8542e66f8481a481ba9c74fa6a31

Aliases

arxiv: 2605.14385 · arxiv_version: 2605.14385v1 · doi: 10.48550/arxiv.2605.14385 · pith_short_12: DCOFXIVOE2QE · pith_short_16: DCOFXIVOE2QEZR2N · pith_short_8: DCOFXIVO

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DCOFXIVOE2QEZR2N6NN2LQIHBU \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 189c5ba2ae26a04cc74df35ba5c1070d248b8542e66f8481a481ba9c74fa6a31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7902b7bc79b12802652183db351695029c55bed14793bc6ab2c083716e8eb056",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-14T05:07:35Z",
    "title_canon_sha256": "c95ed7d6e32421669ff981f4f82a540c11e33b1f50b7ebc1438327f09e95993a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14385",
    "kind": "arxiv",
    "version": 1
  }
}