Open AccessPower convexity of a class of Hessian equations in the ball
Author(s) -
YunHua Ye
Publication year - 2015
Publication title -
global journal of mathematical analysis
Language(s) - English
Resource type - Journals
ISSN - 2307-9002
DOI - 10.14419/gjma.v3i3.5096
Subject(s) - hessian equation , hessian matrix , convexity , mathematics , curvature , ball (mathematics) , gaussian curvature , mathematical analysis , regular polygon , class (philosophy) , principal curvature , convex function , scalar curvature , partial differential equation , geometry , computer science , first order partial differential equation , artificial intelligence , financial economics , economics
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.