31 citations · 115 across the 27 of their papers we have counts for
22 papers · 1 filter
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…
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…
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…
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…
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…
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…
Elliptic PDEs on compact Ricci limit spaces and applications
Shouhei Honda
In this paper we study elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular we establish continuities of…
Cheeger constant, -Laplacian, and Gromov-Hausdorff convergence
Shouhei Honda
We discuss the behavior of with respect to the Gromov-Hausdorff topology and the variable , where is the first positive eigenvalue of the …
Ricci curvature and -convergence
Shouhei Honda
We give the definition of -convergence of tensor fields with respect to the Gromov-Hausdorff topology and several fundamental properties of the convergence. We apply this to e…
A weakly second order differential structure on rectifiable metric measure spaces
Shouhei Honda
We give the definition of angles on a Gromov-Hausdorff limit space of a sequence of complete n-dimensional Riemannian manifolds with a lower Ricci curvature bound. We apply this to…
Ricci curvature and convergence of Lipschitz functions
Shouhei Honda
We give a definition of convergence of differential of Lipschitz functions with respect to measured Gromov-Hausdorff topology. As their applications, we give a characterization of…