Publication date: 10 June 2025
Volume: Vol 60
Issue: Svezak 2
Pages: 327-352
DOI: 10.3336/gm.60.2.08
Glasnik matematički, Vol. 60 No. 2, 2025.
Original scientific paper
https://doi.org/10.3336/gm.60.2.08
Prescribed Weingarten curvature equations in warped product manifolds
Ya Gao
; 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
Chenyang Liu
; Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, China
Jing Mao
; 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
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.
Keywords
Prescribed Weingarten curvature equations, \(k\)-convex, starshaped, warped product manifolds.
Hrčak ID:
342485
URI
Publication date:
20.7.2026.
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