Mathematical Sciences: Global Differential Geometry and Nonlinear Partial Differential Equations

弗拉基米尔奥利克将继续他的研究领域， 非线性整体微分几何及相关问题 偏微分方程他将研究存在， 紧与非紧的唯一性与正则性问题 具有规定曲率函数的完备超曲面。的 重点放在分析方法的基础上的研究， 关于Monge-Ampere方程的问题的一部分 本文研究非线性椭圆型变分问题， 方程也将被研究。 将给定函数实现为 曲率函数基于逐点增长 条件奥利克将尝试用积分代替这些 估算他还将在洛伦兹中寻找相应的结果 空间这些调查将遇到额外的困难， 单位球面不是紧致的

Vladimir Oliker will continue his research in the area of global differential geometry and related problems in nonlinear partial differential equations. He will study existence, uniqueness and regularity problems for compact and noncompact complete hypersurfaces with prescribed curvature functions. The emphasis is placed on the analytic approach based on a study of corresponding questions for Monge-Ampere equations. As a part of this research variational problems for nonlinear elliptic equations will also be investigated. Earlier results on the realization of a given function as a curvature function have been based on pointwise growth conditions. Oliker will attempt to replace these with integral estimates. He will also look for corresponding results in Lorenz space. These investigations will encounter the added difficulty that the unit sphere is not compact.