A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces
In the framework of (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by a positive constant in a synthetic sense, we establish a sharp and rigid reverse-H\"older inequality for first eigenfunctions of the Dirichlet Laplacian. This generalises to the positively curv...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
American Mathematical Society
2022
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| Summary: | In the framework of (possibly non-smooth) metric measure spaces with Ricci
curvature bounded below by a positive constant in a synthetic sense, we
establish a sharp and rigid reverse-H\"older inequality for first
eigenfunctions of the Dirichlet Laplacian. This generalises to the positively
curved and non-smooth setting the classical "Chiti Comparison Theorem". We also
prove a related quantitative stability result which seems to be new even for
smooth Riemannian manifolds. |
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