Gaussian curvature estimates for the convex level sets of p-harmonic functions

2010 ◽  
Vol 63 (7) ◽  
pp. 935-971 ◽  
Author(s):  
Xi-Nan Ma ◽  
Qianzhong Ou ◽  
Wei Zhang
Keyword(s):  
Gaussian Curvature ◽  
Level Sets ◽  
Harmonic Functions ◽  
Curvature Estimates

scholarly journals Level sets of harmonic functions on the Sierpiński gasket

2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Power convexity of a class of Hessian equations in the ball

2015 ◽  
Vol 3 (3) ◽  
pp. 134
Author(s):  
Yunhua Ye
Keyword(s):  
Lower Bound ◽  
Gaussian Curvature ◽  
Principal Curvature ◽  
Power Functions ◽  
Strictly Convex ◽  
Hessian Equations ◽  
Curvature Estimates ◽  
Admissible Solutions ◽  
Special Case

<p>Power convexities of a class of Hessian equations are considered in this paper. It is proved that some power functions of the smooth admissible solutions to the Hessian equations are strictly convex in the ball. For a special case of the equation, a lower bound principal curvature and Gaussian curvature estimates are given.</p>

A Topological Characterization of Conjugate Nets

1977 ◽  
Vol 29 (4) ◽  
pp. 707-721
Author(s):  
Paul A. Vincent
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Function Theory ◽  
Topological Analysis ◽  
Topological Characterization ◽  
Families Of Curves ◽  
Open Maps

One aspect of topological analysis that authors, such as G. T. Whyburn and Marston Morse, have pointed to ([16; 6] for instance) as being fundamental in the development of function theory is the topological study of the level sets of analytic and harmonic functions or of their topological analogues, light open maps and pseudo-harmonic functions. The first step in this direction seems to have been made by H. Whitney [14] when he studied families of curves, given abstractly using a condition of regularity.

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