On the existence of min-max minimal torus

Details On the existence of min-max minimal torus On the existence of min-max minimal torus

2009-04-09

arxiv.org/abs/0904.1461v1

Mathematics

Differential Geometry

31 pages

Scientific paper

In this paper, we will study the existence problem of minmax minimal torus. We use classical conformal invariant geometric variational methods. We prove a theorem about the existence of minmax minimal torus in Theorem 5.1. Firstly we prove a strong uniformization result(Proposition 3.1) using method of [1]. Then we use this proposition to choose good parametrization for our minmax sequences. We prove a compactification result(Lemma 4.1) similar to that of Colding and Minicozzi [2], and then give bubbling convergence results similar to that of Ding, Li and Liu [7]. In fact, we get an approximating result similar to the classical deformation lemma(Theorem 1.1).

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