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Kato meets Bakry-\'Emery
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abstract
We prove that any complete Riemannian manifold with negative part of the Ricci curvature in a suitable Dynkin class is bi-Lipschitz equivalent to a finite-dimensional $\mathrm{RCD}$ space, by building upon the transformation rule of the Bakry-\'Emery condition under time change. We apply this result to show that our previous results on the limits of closed Riemannian manifolds satisfying a uniform Kato bound carry over to limits of complete manifolds. We also obtain a weak version of the Bishop-Gromov monotonicity formula for manifolds satisfying a strong Kato bound.
Forward citations
Cited by 2 Pith papers
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Analysis on surfaces with locally bounded integral curvature
Complete singular surfaces with locally bounded integral curvature are infinitesimally Hilbertian and admit a Hölder heat kernel; under a Dynkin-type negative-curvature bound they are bi-Lipschitz to a surface with cu...
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A sharp spectral splitting theorem
If a complete noncompact n-manifold with at least two ends satisfies lambda1(-gamma Delta + Ric) >= 0 for some gamma < 4/(n-1), then it splits isometrically as R x N with compact N and Ric_N >= 0; the constant is sharp.
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