Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(1): 29-44

Online first article January 19, 2024      Printed January 31, 2024

https://doi.org/10.4134/BKMS.b230001

Copyright © The Korean Mathematical Society.

Rotationally symmetric solutions of the prescribed higher mean curvature spacelike equations in Minkowski spacetime

Man Xu

Northwest Normal University

Abstract

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to $+\infty$. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

Keywords: Higher mean curvature spacelike equation, Minkowski spacetime, rotationally symmetric solutions, topological degree, prolongability theorem

MSC numbers: Primary 34B16, 34B18, 35B08, 35J93

Supported by: This work was supported by the NSFC (No.11671322) and by the grant 21JR1RA230, 2021A-006 and NWNU-LKQN2021-17.