4 papers
Gel'fand's inverse problem under Ricci curvature bounds
Shouhei Honda, Jinpeng Lu
The classical Gel'fand's inverse problem asks whether a Riemannian manifold is uniquely determined by the knowledge of the heat kernel on any open subset of the manifold. We study…
From almost smooth spaces to RCD spaces
Shouhei Honda, Song Sun
We provide various characterizations for a given almost smooth space to be an RCD space, in terms of a local volume doubling and a local Poincaré inequality. Applications include a…
Locally homogeneous RCD spaces
Shouhei Honda, Artem Nepechiy
The goal of this note is to demonstrate how existing results can be adapted to establish the following result: A locally metric measure homogeneous space is iso…
Almost rigidity results of Green functions with non-negative Ricci curvature
Shouhei Honda
This short note provides a survey on rigidity and almost rigidity results of Green functions in a non-smooth setting. We also make some observation on the Cheeger-Yau inequality on…