The $L_p$-Aleksandrov problem for $L_p$-integral curvature

2018 ◽  
Vol 110 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Yong Huang ◽  
Erwin Lutwak ◽  
Deane Yang ◽  
Gaoyong Zhang
Keyword(s):  
Integral Curvature ◽  
Aleksandrov Problem

The Orlicz Aleksandrov Problem for Orlicz Integral Curvature

2020 ◽  
Author(s):  
Yibin Feng ◽  
Binwu He
Keyword(s):  
Integral Curvature ◽  
Basic Properties ◽  
Aleksandrov Problem ◽  
The Given

Abstract In this paper, the Orlicz integral curvature is introduced, and some of its basic properties are discussed. The Orlicz Aleksandrov problem characterizing the Orlicz integral curvature is posed. The problem is solved in two situations when the given measure is even.

A note on a three-dimensional sphere theorem with integral curvature condition

2016 ◽  
Vol 18 (04) ◽  
pp. 1550070 ◽  
Author(s):  
Mijia Lai
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Space Form ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Integral Curvature ◽  
Spherical Space ◽  
Sphere Theorem ◽  
Curvature Condition ◽  
Spherical Space Form

In this paper, we obtain a three-dimensional sphere theorem with integral curvature condition. On a closed three manifold [Formula: see text] with constant positive scalar curvature, if a certain combination of [Formula: see text] norm of the Ricci curvature and [Formula: see text] norm of the scalar curvature is positive, then [Formula: see text] is diffeomorphic to a spherical space form.

On the Aleksandrov problem in linear -normed spaces

2004 ◽  
Vol 59 (7) ◽  
pp. 1001-1011 ◽  
Author(s):  
Hahng-Yun Chu ◽  
Keonhee Lee ◽  
Chun-Gil Park
Keyword(s):  
Normed Spaces ◽  
Aleksandrov Problem
Sign in / Sign up

Export Citation Format

Share Document