Prescribing nearly constant curvatures on balls

Battaglia, Luca; Cruz-Blázquez, Sergio; Pistoia, Angela

doi:10.1017/prm.2023.111

2305.09622.pdf (326.3Kb)

Identificadores

URI: https://hdl.handle.net/10481/85818

DOI: 10.1017/prm.2023.111

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Editorial

Cornell University

Materia

Prescribed curvature

Conformal metrics

Ljapunov-Schmidt construction

Fecha

2023-09-24

Referencia bibliográfica

Published version: Battaglia, L. et al. Prescribing nearly constant curvatures on balls. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2023. [https://doi.org/10.1017/prm.2023.111]

Patrocinador

Spanish Ministry of Universities; Next Generation EU funds PID2021-122122NB-I00; University of Granada; FEDER-MINECO; J. Andalucia FQM-116; University “Sapienza Università di Roma”; Istituto Nazionale di Alta Matematica (INdAM); CUP E55F22000270001

Resumen

In this paper we address two boundary cases of the classical Kazdan- Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of R2, and the scalar and mean curvature on a ball in higher dimensions, via a conformal change of the metric. We deal with the case of negative interior curvature and positive boundary curvature. Using a Ljapunov- Schmidt procedure, we obtain new existence results when the prescribed functions are close to constants.

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