Prescribing Gaussian Curvature on Surfaces with Conical Singularities and Geodesic Boundary

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

doi:10.1007/s10231-022-01274-y

Prescribing Gaussian Curvature on Surfaces with Conical Singularities and Geodesic Boundary

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

Research output: Journal article publication › Journal article › Academic research › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	1173-1185
Number of pages	13
Journal	Annali di Matematica Pura ed Applicata
Volume	202
Issue number	3
DOIs	https://doi.org/10.1007/s10231-022-01274-y
Publication status	Published - Jun 2023

Keywords

Conformal metrics
Conical singularities
Geodesic boundary
Prescribed Gaussian curvature
Variational methods

ASJC Scopus subject areas

Applied Mathematics

More information

10.1007/s10231-022-01274-y

http://hdl.handle.net/10397/99148

Cite this

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title = "Prescribing Gaussian Curvature on Surfaces with Conical Singularities and Geodesic Boundary",

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.",

keywords = "Conformal metrics, Conical singularities, Geodesic boundary, Prescribed Gaussian curvature, Variational methods",

author = "Luca Battaglia and Aleks Jevnikar and Wang, {Zhi An} and Wen Yang",

note = "Funding Information: Open access funding provided by Universit{\`a} degli Studi di Udine within the CRUI-CARE Agreement. W. Yang is partially supported by NSFC No. 12171456, No. 12271369 and No. 11871470. Z.-A. Wang is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU15306121). Publisher Copyright: {\textcopyright} 2022, The Author(s).",

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doi = "10.1007/s10231-022-01274-y",

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AU - Wang, Zhi An

AU - Yang, Wen

N1 - Funding Information: Open access funding provided by Università degli Studi di Udine within the CRUI-CARE Agreement. W. Yang is partially supported by NSFC No. 12171456, No. 12271369 and No. 11871470. Z.-A. Wang is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU15306121). Publisher Copyright: © 2022, The Author(s).

PY - 2023/6

Y1 - 2023/6

N2 - 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.

AB - 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.

KW - Conformal metrics

KW - Conical singularities

KW - Geodesic boundary

KW - Prescribed Gaussian curvature

KW - Variational methods

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Prescribing Gaussian Curvature on Surfaces with Conical Singularities and Geodesic Boundary

Abstract

Keywords

ASJC Scopus subject areas

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