2009/04/09 by Xin Zhou, Zhou, Xin
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.0904.1461
openalex publication_date 2009/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).