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arXiv · 2608.03982

Analysis on surfaces with locally bounded integral curvature

Sebastian Boldt·Batu Güneysu·Maxime Marot
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Abstract

We prove several analytic results on (possibly noncompact) complete singular surfaces having locally bounded integral curvature (in short: BIC surfaces). Regarding these as metric measure spaces with the 2-dimensional Hausdorff measure, we show that these are infinitesimally Hilbertian, locally doubling and satisfy a local Poincar\'e inequality. In particular, this entails the existence of a jointly H\"older continuous heat kernel for the Cheeger Laplacian. Assuming that the negative part of the curvature measure of a BIC surface satisfies a Dynkin-type condition, we show that the surface is bi-Lipschitz equivalent to a BIC surface with a lower bounded curvature measure, entailing global variants of the aforementioned results.

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Sebastian Boldt, Batu Güneysu, Maxime Marot. 2026-08-04. Analysis on surfaces with locally bounded integral curvature. https://arxiv.org/abs/2608.03982

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