Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimization:

Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent Möbius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we establish new geometric expansions of exponentiated small symmetric Clifford tori and analyze the sharp asymptotic behaviour of degenerating tori under the action of the Möbius 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 in the double Schwarzschild space. In a forthcoming paper new existence theorems will be achieved via Morse theory.

本文言語English
ページ(範囲)502-544
ページ数43
ジャーナルProceedings of the London Mathematical Society
115
3
DOI
出版ステータスPublished - 2017 9
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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