论文标题
双曲线空间中的规定曲率测量问题
Prescribed curvature measure problem in hyperbolic space
论文作者
论文摘要
规定的曲率度量的问题是差分几何和非线性部分微分方程中的重要问题之一。在本文中，我们考虑双曲线空间中的规定曲率测量问题。我们通过在双曲线空间中建立对相应的完全非线性PDE的溶液来建立至关重要的C^2规则性估计，从而获得具有规定（N-K）的曲率度量（K <n）的星形K-Convex体。
The problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this paper, we consider prescribed curvature measure problem in hyperbolic space. We obtain the existence of star-shaped k-convex bodies with prescribed (n-k)-th curvature measures (k<n) by establishing crucial C^2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.
