On the instability of minimal submanifolds in Riemannian manifolds of positive curvature

1989 ◽  
Vol 201 (1) ◽  
pp. 33-44
Author(s):  
Takashi Okayasu
Keyword(s):  
Riemannian Manifolds ◽  
Positive Curvature ◽  
Minimal Submanifolds

scholarly journals Cohomogeneity one Riemannian manifolds of non-positive curvature

2007 ◽  
Vol 25 (5) ◽  
pp. 561-581 ◽  
Author(s):  
H. Abedi ◽  
D.V. Alekseevsky ◽  
S.M.B. Kashani
Keyword(s):  
Riemannian Manifolds ◽  
Positive Curvature ◽  
Cohomogeneity One

scholarly journals Curvature estimates for stable free boundary minimal hypersurfaces

2020 ◽  
Vol 2020 (759) ◽  
pp. 245-264 ◽  
Author(s):  
Qiang Guang ◽  
Martin Man-chun Li ◽  
Xin Zhou
Keyword(s):  
Free Boundary ◽  
Riemannian Manifolds ◽  
A Priori ◽  
Minimal Submanifolds ◽  
Manifolds With Boundary ◽  
Curvature Estimate ◽  
Minimal Hypersurfaces ◽  
Curvature Estimates ◽  
Minimal Laminations ◽  
Uniform Area

AbstractIn this paper, we prove uniform curvature estimates for immersed stable free boundary minimal hypersurfaces satisfying a uniform area bound, which generalize the celebrated Schoen–Simon–Yau interior curvature estimates up to the free boundary. Our curvature estimates imply a smooth compactness theorem which is an essential ingredient in the min-max theory of free boundary minimal hypersurfaces developed by the last two authors. We also prove a monotonicity formula for free boundary minimal submanifolds in Riemannian manifolds for any dimension and codimension. For 3-manifolds with boundary, we prove a stronger curvature estimate for properly embedded stable free boundary minimal surfaces without a-priori area bound. This generalizes Schoen’s interior curvature estimates to the free boundary setting. Our proof uses the theory of minimal laminations developed by Colding and Minicozzi.

scholarly journals A Kähler Einstein structure on the tangent bundle of a space form

2001 ◽  
Vol 25 (3) ◽  
pp. 183-195 ◽  
Author(s):  
Vasile Oproiu
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Tangent Bundle ◽  
Negative Curvature ◽  
Space Form ◽  
Positive Curvature ◽  
Holomorphic Sectional Curvature ◽  
Zero Section ◽  
Constant Negative Curvature ◽  
Constant Positive Curvature

We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive curvature.

scholarly journals Examples of Riemannian manifolds with positive curvature almost everywhere

1999 ◽  
Vol 3 (1) ◽  
pp. 331-367 ◽  
Author(s):  
Peter Petersen ◽  
Frederick Wilhelm
Keyword(s):  
Riemannian Manifolds ◽  
Positive Curvature ◽  
Almost Everywhere
Sign in / Sign up

Export Citation Format

Share Document