A class of prescribed Weingarten curvature equations in Euclidean space

Abstract

In this article, we consider a class of prescribed Weingarten curvature equations. Under some sufficient conditions, we obtain an existence result by the standard degree theory based on the a priori estimates for the solutions to the prescribed Weingarten curvature equations.

Keywords:

• k-convex
• prescribed Weingarten curvature
• star-shaped

2010 Mathematics Subject Classification:

• Primary: 35J96, 52A39; Secondary: 53A05

Additional information

Funding

This research was supported by funds from Hubei Provincial Department of Education Key Projects D20181003; Natural Science Foundation of Hubei Province, China [grant no. 2020CFB606 and 2020CFB246].