Small spheres with prescribed nonconstant mean curvature in Riemannian manifolds
Given a function f on a smooth Riemannian manifold without boundary, we prove that if p∈M is a non-degenerate critical point of f, then a neighborhood of p contains a foliation by spheres with mean curvature proportional to f. This foliation is essentially unique. The nondegeneracy assumption can be...
| Authors: | , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2024 |
| Country: | España |
| Institution: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repository: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/380750 |
| Online Access: | http://hdl.handle.net/10261/380750 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85189541005&doi=10.1016%2fj.jfa.2024.110415&partnerID=40&md5=a1a3cdb5880a0fc226ca3f512292b39a |
| Access Level: | Open access |
| Keyword: | Foliation Lyapunov–Schmidt Mean curvature Riemannian manifold |
| Summary: | Given a function f on a smooth Riemannian manifold without boundary, we prove that if p∈M is a non-degenerate critical point of f, then a neighborhood of p contains a foliation by spheres with mean curvature proportional to f. This foliation is essentially unique. The nondegeneracy assumption can be substantially relaxed, at the expense of losing the property that the family of spheres with prescribed mean curvature defines a foliation. © 2024 Elsevier Inc. |
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