On the topology and index of minimal surfaces
| Autor: | Otis Chodosh, Davi Maximo |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Surface (mathematics) Linear function (calculus) Algebra and Number Theory Minimal surface 010102 general mathematics 01 natural sciences Upper and lower bounds Combinatorics Mathematics - Analysis of PDEs Differential Geometry (math.DG) Bounded function Genus (mathematics) 0103 physical sciences FOS: Mathematics Total curvature Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Analysis Topology (chemistry) Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | J. Differential Geom. 104, no. 3 (2016), 399-418 |
| ISSN: | 0022-040X |
| DOI: | 10.4310/jdg/1478138547 |
| Popis: | We show that for an immersed two-sided minimal surface in $\mathbb{R}^3$, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in $\mathbb{R}^3$ of index $2$, as conjectured by Choe. Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface. |
| Databáze: | OpenAIRE |
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