works on
contraction conjecture 1convex hypersurfaces 1inverse mean curvature flow 1lipschitz contractions 1spectral comparison 1

From the 1 of 12 linked papers with an AI index.

collaborators

12 papers

math.MG2026

Heat Codimension and Scalar Curvature

Bang-Xian Han

Motivated by recent proofs of Gromov's codimension-two volume-growth conjecture, we propose a synthetic theory for scalar lower bound on metric measure Dirichlet spaces.

math.MG2026

Lipschitz regularity of harmonic map heat flows from spaces into spaces

Bang-Xian Han, Hui-Chun Zhang, Xi-Ping Zhu

We prove positive-time regularity for harmonic map heat flows from finite-dimensional spaces into complete spaces, without assuming that eithe…

math.DG2026

Contraction Maps Generated by Inverse Mean Curvature Flow

Bang-Xian Han, Zhuo-Nan Zhu

The paper constructs area‑preserving Lipschitz contraction maps using inverse mean curvature flow, providing contractions from spheres to convex hypersurfaces and from disks to con…

math.PR2026

Sharp Poincaré Interpolation Along Wasserstein Geodesics

Bang-Xian Han, Zhuo-Nan Zhu

We prove a sharp interpolation inequality for the Poincaré constant along quadratic Wasserstein geodesics. Let , , be -strongly log-concave probability measures…

math.MG2026

Weak Quadruple Comparison and Structure Theory Beyond Alexandrov Geometry

Bang-Xian Han, Liming Yin

We introduce a new four-point comparison principle, called the -weak quadruple condition, for non-Riemannian spaces with synthetic non-negative curvature. This co…

math.MG2026

Wasserstein Barycenter Convexity Detects Hilbertian Geometry

Bang-Xian Han, Deng-Yu Liu

We prove that convexity of the Boltzmann entropy at Wasserstein barycenters is strong enough to distinguish Hilbert spaces from general Banach spaces. Thus Wasserstein barycenters…