English

Prescribing curvatures on surfaces with conical singularities and corners

Analysis of PDEs 2025-08-18 v2 Differential Geometry

Abstract

This paper is concerned with the problem of prescribing Gaussian curvature and geodesic curvature in a compact surface with boundary with conical singularities and corners. Solutions are obtained using a new variational formulation, recently introduced for the regular counterpart of the problem and extended here to the singular case. As far as we know, this is the first result for the problem of prescribed curvatures in surfaces with singularities.

Keywords

Cite

@article{arxiv.2502.15976,
  title  = {Prescribing curvatures on surfaces with conical singularities and corners},
  author = {Luca Battaglia and Francisco Javier Reyes-Sanchez},
  journal= {arXiv preprint arXiv:2502.15976},
  year   = {2025}
}

Comments

37 pages

R2 v1 2026-06-28T21:53:37.031Z