Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces

By K. Kuwae, Yoshiroh Machigashira, T. Shioya. 2001

123 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/509ea8949f8751e0d03c3b69c14179116505df44

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Yau's gradient estimates on Alexandrov spaces (2010, methodology): “ we have, for almost all r ∈ (0,δ0), (2.15) ? ∂Bp(r) f(x) − f(p) dvol(x) = r2 2 · ? Σp Hp f(ξ,ξ)dξ+o(r2). 2.2. Sobolev spaces. Several diﬀerent notions of Sobolev spaces have been established, see[8, 19, 43, 20, 24]1. They coincide each other on Alexandrov spaces. Let M be an n-dimensional Alexand”
The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions (2003, unknown): “(See e.g. [Gro99],[ KMS01 ], [KS01] and the references therein.)”
Ricci curvature and $L^p$-convergence (2012, methodology): “Awith respect to A if and only if so is fwith respect to Aˆ, Γ 1(Tr sA;A) = Γ1(Tr sA;Aˆ) and so on. Remark 2.9. It is known that similar results given here hold on Alexandrov spaces. See for instance [3, 33, 40, 41, 42, 43]. RICCI CURVATURE 11 2.5. Limit spaces of Riemannian manifolds. In this subse”
Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K, N)$-spaces (2017, background): “See for instance [20,53] for constructions of isospectral manifolds and of isospectral Alexandrov spaces (see also [38] for analysis on Alexandrov spaces).”
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres (2011, unknown): “ the tangent space to M = G=H at the left coset eH of the identity 5For the foundational material on spectral theory for the Laplacian on Alexandrov spaces, we refer to Kuwae, Machigashira and Shioya [21]. 6In fact, these limits ought to have more properties than the usual Gromov-Hausdor limit of a ”