Semantic Scholar Open Access 2009 13 sitasi

On the Existence of Min-Max Minimal Torus

Xin Zhou

Abstrak

In this paper, we will study the existence problem of min-max minimal torus. We use classical conformal invariant geometric variational methods. We prove a theorem about the existence of min-max minimal torus in Theorem 5.1. First we prove a strong uniformization result (Proposition 3.1) using the method of Ahlfors and Bers (Ann. Math. 72(2):385–404, 1960). Then we use this proposition to choose good parameterization for our min-max sequences. We prove a compactification result (Lemma 4.1) similar to that of Colding and Minicozzi (Width and finite extinction time of Ricci flow, 0707.0108 [math.DG], 2007), and then give bubbling convergence results similar to that of Ding et al. (Invent. math. 165:225–242, 2006). In fact, we get an approximating result similar to the classical deformation lemma (Theorem 1.1).

Topik & Kata Kunci

Mathematics

Penulis (1)

Xin Zhou

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Zhou, X. (2009). On the Existence of Min-Max Minimal Torus. https://doi.org/10.1007/S12220-010-9137-0

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Informasi Jurnal

Tahun Terbit: 2009
Bahasa: en
Total Sitasi: 13×
Sumber Database: Semantic Scholar
DOI: 10.1007/S12220-010-9137-0
Akses: Open Access ✓