Analysis on surfaces with locally bounded integral curvature

Sebastian Boldt; Batu Güneysu; Maxime Marot

Analysis on surfaces with locally bounded integral curvature

Differential Geometry 2026-08-04 v1 Metric Geometry

Authors: Sebastian Boldt , Batu Güneysu , Maxime Marot

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.

Cite

@article{arxiv.2608.03982,
  title  = {Analysis on surfaces with locally bounded integral curvature},
  author = {Sebastian Boldt and Batu Güneysu and Maxime Marot},
  journal= {arXiv preprint arXiv:2608.03982},
  year   = {2026}
}