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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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4 results for “mGH-convergence”

Super-Ricci Flows for Metric Measure Spacesmath.DG

Introduces new flows for metric measure spaces, proving stability and compactness.

problem Stability and compactness of metric measure spaces.

method Introduces super-Ricci flows and Ricci flows, proving stability and compactness under mGH-convergence.

result Uniformly bounded families of super-Ricci flows are compact.

Super-Ricci flows Metric measure spaces Stability Compactness mGH-convergence

2016-03-07abs ↗pdf ↗

Short-time behavior of the heat kernel and Weyl's law on

RCD^*(K, N)

-spacesmath.MG

The paper studies heat kernel behavior in RCD spaces and initiates Weyl's law study.

problem Understanding heat kernel behavior in RCD spaces.

method Proved pointwise convergence of heat kernels for mGH-convergent sequences of RCD spaces.

result Initiated study of Weyl's law in RCD spaces.

heat kernel RCD spaces Weyl's law short-time behavior

2017-01-14abs ↗pdf ↗

Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature boundsmath.DG

Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds.

problem Characterizing and proving rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds.

method Analysis of Riemannian manifolds and metric measure spaces with synthetic lower Ricci curvature bounds, using concentration compactness and Polya-Szego inequalities.

result Closed Riemannian manifolds with optimal Sobolev constant are isometric to the sphere, and almost equality implies close measure Gromov-Hausdorff convergence to a spherical suspension.

Sobolev inequalities Riemannian manifolds lower Ricci curvature bounds measure Gromov-Hausdorff convergence Sobolev constant

2021-08-04abs ↗pdf ↗

Boundary regularity and stability for spaces with Ricci bounded belowmath.DG

The paper examines the structure and stability of boundaries in noncollapsed RCD spaces.

problem Structuring and stability of boundaries in noncollapsed RCD spaces.

method Effective measure bounds and ε-regularity theorem.

result The boundary is homeomorphic to a manifold away from a set of codimension 2 and is

N-1

rectifiable.

RCD spaces noncollapsed spaces boundary structure ε-regularity rectifiability

2020-11-17abs ↗pdf ↗