COMPLETE STATIONARY SURFACES IN ${\mathbb R}^4_1$ WITH TOTAL GAUSSIAN CURVATURE – ∫ KdM = 4π

DOI10.1142/S0129167X13500882zbMath1307.53006arXiv1210.8254OpenAlexW3102842047MaRDI QIDQ5396079

Xiang Ma, Peng Wang

Publication date: 5 February 2014

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.8254

zbMATH Keywords

Weierstrass representationtotal Gaussian curvaturestationary surface

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Non-Euclidean differential geometry (53A35)

Cites Work

• Unnamed Item
• On subharmonic functions and differential geometry in the large
• The topology of complete minimal surfaces of finite total Gaussian curvature
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• The classification of complete minimal surfaces in \(R^ 3\) with total curvature greater than -8pi
• Classification of complete minimal surfaces in \(R^ 3\) with total curvature 12\(\pi\)
• Global geometry and topology of spacelike stationary surfaces in the 4-dimensional Lorentz space
• Curvature properties of zero mean curvature surfaces in four-dimensional Lorentzian space forms

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