Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ROTATIONALLY SYMMETRIC SOLUTIONS OF THE PRESCRIBED HIGHER MEAN CURVATURE SPACELIKE EQUATIONS IN MINKOWSKI SPACETIME

  • Man Xu (College of Mathematics and Statistics Northwest Normal University)
  • Received : 2023.01.01
  • Accepted : 2023.04.21
  • Published : 2024.01.31
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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 + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

Keywords

Acknowledgement

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

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