The Dirichlet problem for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

Ya Gao; YanLing Gao; Jing Mao

The Dirichlet problem for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

Differential Geometry 2021-11-04 v1

Authors: Ya Gao , YanLing Gao , Jing Mao

Abstract

In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$ , which can be seen as a prescribed curvature problem and a continuous work of [12].

Keywords

Hessian quotient equations Dirichlet problem Lorentz-Minkowski space prescribed curvature existence and uniqueness

Cite

@article{arxiv.2111.02028,
  title  = {The Dirichlet problem for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$},
  author = {Ya Gao and YanLing Gao and Jing Mao},
  journal= {arXiv preprint arXiv:2111.02028},
  year   = {2021}
}

Comments

27 pages. Comments are welcome. arXiv admin note: substantial text overlap with arXiv:2111.01345

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