Minimal Surfaces in Riemannian Manifolds

1994 ◽  
pp. 104-110
Author(s):  
Guangyin Wang
Keyword(s):  
Riemannian Manifolds ◽  
Minimal Surfaces

scholarly journals Bifurcation of minimal surfaces in Riemannian manifolds

1995 ◽  
Vol 347 (1) ◽  
pp. 51-62 ◽  
Author(s):  
Jürgen Jost ◽  
Xianqing Li-Jost ◽  
Xiao Wei Peng
Keyword(s):  
Riemannian Manifolds ◽  
Minimal Surfaces

scholarly journals Self-intersections of closed parametrized minimal surfaces in generic Riemannian manifolds

2021 ◽  
Author(s):  
John Douglas Moore
Keyword(s):  
Minimal Surface ◽  
Riemannian Manifolds ◽  
Minimal Surfaces ◽  
Measure Theory ◽  
Complex Structure ◽  
Geometric Measure Theory ◽  
Riemannian Metric ◽  
Oriented Manifold ◽  
Geometric Measure

AbstractThis article shows that for generic choice of Riemannian metric on a compact oriented manifold M of dimension four, the tangent planes at any self-intersection $$p \in M$$ p ∈ M of any prime closed parametrized minimal surface in M are not simultaneously complex for any orthogonal complex structure on M at p. This implies via geometric measure theory that $$H_2(M;{{\mathbb {Z}}})$$ H 2 ( M ; Z ) is generated by homology classes that are represented by oriented imbedded minimal surfaces.

Sign in / Sign up

Export Citation Format

Share Document