Constructs uncountably many pairwise conformally inequivalent non-rotationally symmetric type II ancient Yamabe flows on S^n (n≥3) via non-radial inner-outer gluing after stereographic projection.
A proof for the Riemannian positive mass theorem up to dimension 19
11 Pith papers cite this work. Polarity classification is still indexing.
11
Pith papers citing it
years
2026 11representative citing papers
Introduces a boundary analogue of the Gauss-Bonnet-Chern mass for asymptotically flat half-manifolds, proves it is well-defined, establishes positive mass theorems for graphical and conformally flat graphs, and provides a Penrose-type inequality.
Asymptotically flat L^∞ ∩ W^{1,n} manifolds with non-negative distributional scalar curvature satisfy the positive mass theorem, with zero mass implying global isometry to Euclidean space via an integral distance.
Overtorical manifolds and sufficiently regular enlargeable AM–PI spaces admit no positive (weighted) scalar curvature, proved by singular dimension descent with conformal blow-ups.
The Riemannian Penrose inequality is proven in arbitrary dimensions for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary allowing singular sets of Hausdorff dimension at most n-8, with equality only for Riemannian Schwarzs
A new inductive dimension descent scheme extends the Schoen-Yau positive mass theorem to arbitrary dimensions using shielding principles, conformal blow-ups, and Cheeger-Naber singular set bounds.
ADM mass is nonnegative (and zero only for Euclidean space under a slightly stronger dimension bound) for complete AF L∞ metrics with nonnegative scalar curvature outside a singular set of Minkowski dimension < n−3+2/n.
The positive mass theorem holds for complete asymptotically hyperbolic manifolds satisfying the dominant energy condition, including those with arbitrary ends.
Proves the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloidal initial data sets in arbitrary dimensions using Brendle-Wang's Riemannian positive mass theorem.
Under a non-surjectivity assumption on the fundamental group homomorphism from the singular set, an L^∞ metric on a torus with non-negative scalar curvature outside a Minkowski dimension ≤ n-3+(n-1)^{-1} singular set extends to a smooth flat metric, proved via weighted scalar curvature and the relat
Defines a spectral mass invariant for AH 3-manifolds with toroidal infinity and proves positivity, rigidity, and band width estimates under spectral scalar curvature lower bounds.
citing papers explorer
-
Uncountably many non-rotationally symmetric type II ancient Yamabe flows on the sphere
Constructs uncountably many pairwise conformally inequivalent non-rotationally symmetric type II ancient Yamabe flows on S^n (n≥3) via non-radial inner-outer gluing after stereographic projection.
-
A new boundary mass for asymptotically flat half-manifolds
Introduces a boundary analogue of the Gauss-Bonnet-Chern mass for asymptotically flat half-manifolds, proves it is well-defined, establishes positive mass theorems for graphical and conformally flat graphs, and provides a Penrose-type inequality.
-
Spaces with distributional scalar curvature bounded from below: Optimal regularity and positive mass
Asymptotically flat L^∞ ∩ W^{1,n} manifolds with non-negative distributional scalar curvature satisfy the positive mass theorem, with zero mass implying global isometry to Euclidean space via an integral distance.
-
Positive Scalar Curvature Obstructions via Singular Dimension Descent
Overtorical manifolds and sufficiently regular enlargeable AM–PI spaces admit no positive (weighted) scalar curvature, proved by singular dimension descent with conformal blow-ups.
-
Riemannian Penrose inequality in all dimensions
The Riemannian Penrose inequality is proven in arbitrary dimensions for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary allowing singular sets of Hausdorff dimension at most n-8, with equality only for Riemannian Schwarzs
-
A dimension descent scheme for the positive mass theorem in arbitrary dimension
A new inductive dimension descent scheme extends the Schoen-Yau positive mass theorem to arbitrary dimensions using shielding principles, conformal blow-ups, and Cheeger-Naber singular set bounds.
-
Riemannian Positive Mass Theorem in All Dimensions in the Presence of Low-Codimension Singularities
ADM mass is nonnegative (and zero only for Euclidean space under a slightly stronger dimension bound) for complete AF L∞ metrics with nonnegative scalar curvature outside a singular set of Minkowski dimension < n−3+2/n.
-
Positive mass theorem for initial data sets with arbitrary ends
The positive mass theorem holds for complete asymptotically hyperbolic manifolds satisfying the dominant energy condition, including those with arbitrary ends.
-
The Hyperboloidal and Spacetime Positive Mass Theorem in All Dimensions
Proves the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloidal initial data sets in arbitrary dimensions using Brendle-Wang's Riemannian positive mass theorem.
-
$L^\infty$-metrics on tori and Schoen's conjecture
Under a non-surjectivity assumption on the fundamental group homomorphism from the singular set, an L^∞ metric on a torus with non-negative scalar curvature outside a Minkowski dimension ≤ n-3+(n-1)^{-1} singular set extends to a smooth flat metric, proved via weighted scalar curvature and the relat
-
Spectral Positive Mass Theorem for Asymptotically Hyperbolic 3-manifolds with Toroidal Infinity
Defines a spectral mass invariant for AH 3-manifolds with toroidal infinity and proves positivity, rigidity, and band width estimates under spectral scalar curvature lower bounds.