Glasnik Matematicki, Vol. 60, No. 2 (2025), 327-352. \( \)

PRESCRIBED WEINGARTEN CURVATURE EQUATIONS IN WARPED PRODUCT MANIFOLDS

Ya Gao, Chenyang Liu and Jing Mao

School of Mathematical Science and Academy for Multidisciplinary Studies, Capital Normal University, Beijing 100048, China,
Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, China
e-mail:Echo-gaoya@outlook.com

Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, China
e-mail:1109452431@qq.com

Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, China,
Key Laboratory of Intelligent Sensing System and Security (Hubei University), Ministry of Education, China
e-mail:jiner120@163.com

Abstract.   In this paper, under suitable settings, we can obtain the existence of solutions to a class of prescribed Weingarten curvature equations in warped product manifolds of special type by the standard degree theory based on the a priori estimates for the solutions. This is to say that the existence of closed hypersurface (which is graphic with respect to the base manifold and whose \(k\)-Weingarten curvature satisfies some constraint) in a given warped product manifold of special type can be assured.

2020 Mathematics Subject Classification.   53C42, 35J60

Key words and phrases.   Prescribed Weingarten curvature equations, \(k\)-convex, starshaped, warped product manifolds.

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https://doi.org/10.3336/gm.60.2.08

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