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EnglishWe construct embedded Willmore tori with small area constra int in Riemannian three-manifolds under some curvature condition used to prevent M ̈obius dege neration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we establish new ge ometric expansions of exponentiated small symmetric Clifford tori and analyze the sharp asymptot ic behavior of degenerating tori under the action of the M ̈obius group. In this first work we prove two existence results by minimizing or maximizing a suitable reduced functional, in particular we obtain embedded area-constrained Willmore tori (or, equivalently, toroidal critical points of the Hawking mass under area-constraint) in compact 3-manifolds with constant scalar curvature and i n the double Schwarzschild space. In a forthcoming paper new existence theorems will be achieved v ia Morse theory.
| Titolo: | Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimization | |
| Autori: | ||
| Data di pubblicazione: | 2017 | |
| Rivista: | ||
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Parole Chiave: | Willmore functional, Willmore tori, Hawking mass, nonlinear fourth order partial differential equations, Lyapunov-Schmidt reduction | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1112/plms.12047 | |
| Handle: | http://hdl.handle.net/1234/56325 http://hdl.handle.net/11384/56325 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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