Isometric immersions of \(\mathrm{RCD}(K, N)\) spaces via heat kernels
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Publication:2696603
DOI10.1007/s00526-023-02460-3OpenAlexW4360979753MaRDI QIDQ2696603
Publication date: 17 April 2023
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2205.11768
Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Cites Work
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- Heat kernel bounds on metric measure spaces and some applications
- Weak and strong convergence of derivations and stability of flows with respect to MGH convergence
- Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
- Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
- Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
- An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
- Ricci curvature and \(L^{p}\)-convergence
- On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
- From volume cone to metric cone in the nonsmooth setting
- Obata's rigidity theorem for metric measure spaces
- Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
- Minimal immersions of compact irreducible homogeneous Riemannian manifolds
- Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
- Embedding Riemannian manifolds by their heat kernel
- On the structure of spaces with Ricci curvature bounded below. I
- Local spectral convergence in \(\mathrm{RCD}^\ast(K, N)\) spaces
- Sobolev spaces on warped products
- Recognizing the flat torus among \(\mathsf{RCD}^*(0,N)\) spaces via the study of the first cohomology group
- Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces
- Heat kernels and Green's functions on limit spaces
- Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
- Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
- On the topology and the boundary of \(N\)-dimensional \(\mathsf{RCD}\,(K,N)\) spaces
- Isometric immersions of RCD spaces
- Weakly non-collapsed RCD spaces are strongly non-collapsed
- Partial derivatives in the nonsmooth setting
- Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces
- Weyl's law on \(RCD^{\ast} (K, N)\) metric measure spaces
- A sufficient condition to a regular set being of positive measure on spaces
- On the universal cover and the fundamental group of an \(\mathsf{RCD}^\ast(K,N)\)-space
- Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces
- Cones over metric measure spaces and the maximal diameter theorem
- Ricci curvature for metric-measure spaces via optimal transport
- Structure theory of metric measure spaces with lower Ricci curvature bounds
- Cheeger-harmonic functions in metric measure spaces revisited
- Metric measure spaces with Riemannian Ricci curvature bounded from below
- On the measure contraction property of metric measure spaces
- On the geometry of metric measure spaces. I
- On the geometry of metric measure spaces. II
- Minimal immersions of Riemannian manifolds
- Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions
- On the differential structure of metric measure spaces and applications
- Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
- Non-Gaussian Aspects of Heat Kernel Behaviour
- Non-collapsed spaces with Ricci curvature bounded from below
- Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
- New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
- Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
- A Note About the Strong Maximum Principle on RCD Spaces