用偏微分方程组刻画旋转二次曲面
A characterization of revolution quadrics by a system of partial differential equations
摘要：
本文证明了在完备连通黎曼流形上二阶偏微分方程非线性系统整体解的存在性具有拓扑和几何意义，并且在该解的正性区域内，其倒数是$\Rn$中下列旋转对称超曲面之一的径向函数：抛物面、椭圆面、双叶双曲面的一个片和超平面。
英文摘要：
It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such solution its reciprocal is the radial function of only one of the following rotationally symmetric hypersurfaces in $\Rn$: paraboloid, ellipsoid, one sheet of a two-sheeted hyperboloid, and a hyperplane.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
