Failure of strong unique continuation for harmonic functions on RCD spaces
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Publication:2681768
DOI10.1515/crelle-2022-0090OpenAlexW4311400238MaRDI QIDQ2681768
Publication date: 7 February 2023
Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2204.13889
Second-order elliptic equations (35J15) Elliptic equations on manifolds, general theory (58J05) Differential geometric aspects of harmonic maps (53C43) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)
Cites Work
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- Characterization of low dimensional \(RCD^\ast(K, N)\) spaces
- Three circles theorems for harmonic functions
- Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
- Nonlinear potential theory on metric spaces
- A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
- A unique continuation theorem for exterior differential forms on Riemannian manifolds
- Smoothness of the metric of spaces with two-sided bounded Aleksandrov curvature
- Characterization of absolutely continuous curves in Wasserstein spaces
- On the unique continuation property of elliptic divergence form equations in the plane
- Harmonic functions on manifolds
- On the generic eigenvalue flow of a family of metrics and its application
- Differentiability of Lipschitz functions on metric measure spaces
- The Riemannian structure of Alexandrov spaces
- Parallel transportation for Alexandrov space with curvature bounded below
- On the structure of spaces with Ricci curvature bounded below. I
- Harmonic functions with polynomial growth
- On the structure of spaces with Ricci curvature bounded below. II
- On the structure of spaces with Ricci curvature bounded below. III
- DC calculus
- Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients
- Harmonic functions of polynomial growth on complete manifolds. II
- Second order differentiation formula on \(\mathsf{RCD}^*(K,N)\) spaces
- Weakly non-collapsed RCD spaces are strongly non-collapsed
- On the structure of RCD spaces with upper curvature bounds
- CD meets CAT
- The globalization theorem for the curvature-dimension condition
- 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 geometry of metric measure spaces. I
- On the geometry of metric measure spaces. II
- Linear and quasilinear elliptic equations
- New formulas for the Laplacian of distance functions and applications
- Singularities and diffeomorphisms
- Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients
- Harmonic functions of polynomial growth on singular spaces with nonnegative Ricci curvature
- Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
- Unique continuation for elliptic operators: A geometric-variational approach
- Differential equations on riemannian manifolds and their geometric applications
- On Courant's nodal domain theorem
- Elliptic Equations in Divergence Form, Geometric Critical Points of Solutions, and Stekloff Eigenfunctions
- An existence theorem of harmonic functions with polynomial growth
- Non-collapsed spaces with Ricci curvature bounded from below
- Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds
- Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
- Convergence of Alexandrov spaces and spectrum of Laplacian
- Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces