scholarly journals Curvature estimates for submanifolds with prescribed Gauss image and mean curvature

2009 ◽  
Vol 37 (3-4) ◽  
pp. 385-405 ◽  
Author(s):  
Y. L. Xin
Keyword(s):  
Mean Curvature ◽  
Gauss Image ◽  
Curvature Estimates

scholarly journals On the mean curvature estimates for bounded submanifolds

1992 ◽  
Vol 114 (4) ◽  
pp. 1173-1173 ◽  
Author(s):  
Leslie Coghlan ◽  
Yoe Itokawa ◽  
Roman Kosecki
Keyword(s):  
Mean Curvature ◽  
Curvature Estimates ◽  
The Mean

On submanifolds of highly negatively curved spaces

2014 ◽  
Vol 25 (06) ◽  
pp. 1450055
Author(s):  
G. Pacelli Bessa ◽  
Stefano Pigola ◽  
Alberto G. Setti
Keyword(s):  
Mean Curvature ◽  
Curved Spaces ◽  
Negatively Curved ◽  
Curvature Estimates ◽  
Isoperimetric Ratio

We prove spectral, stochastic and mean curvature estimates for complete m-submanifolds φ : M → N of n-manifolds with a pole N in terms of the comparison isoperimetric ratio Im and the extrinsic radius rφ ≤ ∞. Our proof holds for the bounded case rφ < ∞, recovering the known results, as well as for the unbounded case rφ = ∞. In both cases, the fundamental ingredient in these estimates is the integrability over (0, rφ) of the inverse [Formula: see text] of the comparison isoperimetric radius. When rφ = ∞, this condition is guaranteed if N is highly negatively curved.

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