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arXiv · 0904.1461

On the existence of min-max minimal torus

Xin Zhou
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Abstract

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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Xin Zhou. 2009-04-09. On the existence of min-max minimal torus. https://arxiv.org/abs/0904.1461

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