10 citations · 11 across the 4 of their papers we have counts for
11 papers
Hypercontractivity of the heat flow on spaces: sharpness and rigidities
Shouhei Honda, Alexandru Kristály, Alexandru Pîrvuceanu
The main goal of the present paper is to provide sharp hypercontractivity bounds of the heat flow on metric measure spaces. The best consta…
Isometric immersions of RCD spaces
Shouhei Honda
We prove that if an RCD space has a regular isometric immersion in a Euclidean space, then the immersion is a locally bi-Lipschitz embedding map. This result leads us to prove that…
Collapsed Ricci limit spaces as non-collapsed spaces
Shouhei Honda
In this short note we provide several conjectures on the regularity of measured Gromov-Hausdorff limit spaces of Riemannian manifolds with Ricci curvature bounded below, from the p…
Sphere theorems for RCD and stratified spaces
Shouhei Honda, Ilaria Mondello
We prove topological sphere theorems for RCD(n-1, n) spaces which generalize Colding's results and Petersen's result to the RCD setting. We also get an improved sphere theorem in t…
New differential operator and non-collapsed spaces
Shouhei Honda
We show characterizations of non-collapsed compact spaces, which in particular confirm a conjecture of De Philippis-Gigli on the implication from the weakly non-collaps…
Embedding of spaces in via eigenfunctions
Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies +1
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results by Bérard, Bé…