Power convexity of a class of Hessian equations in the ball
DOI:
https://doi.org/10.14419/gjma.v3i3.5096Keywords:
Admissible solution, Hessian equations, Power convexity, Strict convexity.Abstract
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.
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Received date: July 21, 2015
Accepted date: August 23, 2015
Published date: August 24, 2015