Prescribing Gaussian Curvature on Surfaces with Conical Singularities and Geodesic Boundary

Luca Battaglia, Aleks Jevnikar, Zhi An Wang, Wen Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

We study conformal metrics with prescribed Gaussian curvature on surfaces with conical singularities and geodesic boundary in supercritical regimes. Exploiting a variational argument, we derive a general existence result for surfaces with at least two boundary components. This seems to be the first result in this setting. Moreover, we allow to have conical singularities with both positive and negative orders, that is cone angles both less and greater than 2 π.

Original languageEnglish
Pages (from-to)1173-1185
Number of pages13
JournalAnnali di Matematica Pura ed Applicata
Volume202
Issue number3
DOIs
Publication statusPublished - Jun 2023

Keywords

  • Conformal metrics
  • Conical singularities
  • Geodesic boundary
  • Prescribed Gaussian curvature
  • Variational methods

ASJC Scopus subject areas

  • Applied Mathematics

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