NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY

被引：15

作者：

Alarcon, Antonio ^{[1
,2
]}

Forstneric, Franc ^{[3
,4
]}

机构：

[1] Univ Granada, Dept Geometria & Topol, Campus Fuentenueva S-N, E-18071 Granada, Spain

[2] Univ Granada, Inst Matemat IEMath GR, Campus Fuentenueva S-N, E-18071 Granada, Spain

[3] Univ Ljubljana, Fac Math & Phys, Jadranska 19, SI-1000 Ljubljana, Slovenia

[4] Inst Math Phys & Mech, Jadranska 19, SI-1000 Ljubljana, Slovenia

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2019年 / 106卷 / 03期

关键词：

minimal surface; Riemann surface; Oka manifold; GAUSS MAP; CONJECTURES; CURVATURE; MANIFOLDS; EXISTENCE; TOPOLOGY; GEOMETRY;

D O I：

10.1017/S1446788718000125

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we survey recent developments in the classical theory of minimal surfaces in Euclidean spaces which have been obtained as applications of both classical and modern complex analytic methods; in particular, Oka theory, period dominating holomorphic sprays, gluing methods for holomorphic maps, and the Riemann-Hilbert boundary value problem. Emphasis is on results pertaining to the global theory of minimal surfaces, in particular, the Calabi-Yau problem, constructions of properly immersed and embedded minimal surfaces in R-n and in minimally convex domains of R-n, results on the complex Gauss map, isotopies of conformal minimal immersions, and the analysis of the homotopy type of the space of all conformal minimal immersions from a given open Riemann surface.

引用

页码：287 / 341

页数：55

共 110 条

[31] One-sided minimal surfaces with a given boundary [J].