31 citations · 115 across the 27 of their papers we have counts for
29 papers
Regularity and structure of spaces with synthetic Ricci bounds and positive injectivity radius
Shouhei Honda, Ruobing Zhang
In the paper, we develop a structure theory for metric measure spaces with synthetic lower Ricci curvature bounds, known as RCD spaces. Under a positive injectivity-radius assumpti…
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…
Gromov-Hausdorff stability of tori under Ricci and integral scalar curvature bounds
Shouhei Honda, Christian Ketterer, Ilaria Mondello +2
We establish a nonlinear analogue of a splitting map into a Euclidean space, as a harmonic map into a flat torus. We prove that the existence of such a map implies Gromov-Hausdorff…
Sharp gradient estimate, rigidity and almost rigidity of Green functions on non-parabolic spaces
Shouhei Honda, Yuanlin Peng
Inspired by a result of Colding, the present paper studies the Green function on a non-parabolic space for some finite …
Spectral distances on RCD spaces
Shouhei Honda
We provide relationships between the spectral convergences in Bérard-Besson-Gallot sense, in Kasue-Kumura sense and the measured Gromov-Hausdorff convergence, for compact finite di…
Singular Weyl's law with Ricci curvature bounded below
Xianzhe Dai, Shouhei Honda, Jiayin Pan +1
We establish two surprising types of Weyl's laws for some compact /Ricci limit spaces. The first type could have power growth of any order (bigger than one). Th…
A note on the topological stability theorem from RCD spaces to Riemannian manifolds
Shouhei Honda, Yuanlin Peng
Inspired by a recent work of Wang-Zhao, in this note we prove that for a fixed -dimensional closed Riemannian manifold , if an space $(X, \mathsf{…
Weakly non-collapsed RCD spaces are strongly non-collapsed
Camillo Brena, Nicola Gigli, Shouhei Honda +1
We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second…
Sobolev mappings between RCD spaces and applications to harmonic maps: a heat kernel approach
Shouhei Honda, Yannick Sire
We investigate a Sobolev map from a finite dimensional RCD space $(X, \dist_X, \meas_X)$ to a finite dimensional non-collapsed compact RCD space $(Y, \dist_Y, \mathcal{H}^N)$.…
Density and non-density of on complete manifolds with curvature bounds
Shouhei Honda, Luciano Mari, Michele Rimoldi +1
We investigate the density of compactly supported smooth functions in the Sobolev space on complete Riemannian manifolds. In the first part of the paper, we extend to the…
A characterization of non-collapsed spaces via Einstein tensors
Shouhei Honda, Xingyu Zhu
We investigate the second principal term in the expansion of metrics induced by heat kernel embedding into on a compact space. We prove that…
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…
Bakry-Émery conditions on almost smooth metric measure spaces
Shouhei Honda
In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition . The sufficient condition is sat…
Continuity of nonlinear eigenvalues in spaces with respect to measured Gromov-Hausdorff convergence
Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies
In this note we prove in the nonlinear setting of spaces the stability of the Krasnoselskii spectrum of the Laplace operator under measured Gromov-Hausdorff con…
Local spectral convergence in spaces
Luigi Ambrosio, Shouhei Honda
In this note we give necessary and sufficient conditions for the validity of the local spectral convergence, in balls, on the -setting.
Short-time behavior of the heat kernel and Weyl's law on -spaces
Luigi Ambrosio, Shouhei Honda, David Tewodrose
In this paper, we prove pointwise convergence of heat kernels for mGH-convergent sequences of -spaces. We obtain as a corollary results on the short-time behavior of th…
Ricci curvature and Orientability
Shouhei Honda
In this paper we define an orientation of a measured Gromov-Hausdorff limit space of Riemannian manifolds with uniform Ricci bounds from below. This is the first observation of ori…
New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
Luigi Ambrosio, Shouhei Honda
The aim of this paper is to provide new stability results for sequences of metric measure spaces convergent in the measured Gromov-Hausdorff sense. By adopting the…
Spectral convergence under bounded Ricci curvature
Shouhei Honda
For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on th…
Fano-Ricci limit spaces and spectral convergence
Akito Futaki, Shouhei Honda, Shunsuke Saito
We study the behavior under Gromov-Hausdorff convergence of the spectrum of weighted $\barpartial$-Laplacian on compact Kähler manifolds. This situation typically occurs for a sequ…