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

Man Xu
대한수학회 (The Korean Mathematical Society)|2024.01|대한수학회보 (Bulletin of the KMS)|제61권 제1호|pp. 29-44|DOI 10.4134/BKMS.b230001

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참고문헌

키워드

Minkowski spacetimeHigher mean curvature spacelike equationrotationally symmetric solutionstopological degreeprolongability theorem
주제분류수학

초록

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.

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.

참고문헌 (37)

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