Mathematical Sciences: Classical and Applied Analysis

9401167康库斯该奖项支持对液桥、(不对称)悬垂液滴和缓慢旋转的流体质量的毛细理论和几何问题的数学研究。我们还将研究楔形域和鼻状域中曲率类型曲面的奇异行为以及H图的先验曲率估计。其中一些调查将与美国国家航空航天局和欧洲航天局合作，与空间实验有关。其他与斯坦福-洛克希德引力B联合实验有关，该实验使用轨道陀螺仪测试广义相对论，以及斯坦福大学关于引力和惯性质量等效原理的实验。这些研究将包括参考计算，但工作的基本内容将是数学的。形式理论是从一个完全严格的角度发展起来的，包括从几何角度分析偏微分方程解。由此产生的实验可以被视为对数学形式主义所基于的基本物理假设的精确测试。反过来，物理问题继续提出新的数学问题。***

9401167 Concus This award supports mathematical research on capillarity theory and geometrical questions for liquid bridges, for (asymmetric) pendent liquid drops and for slowly rotating fluid masses. Exotic behavior for surfaces of curvature type in wedges and proboscis domains and a-priori curvature estimates for H-graphs will also be studied. Some of these investigations are to be conducted in connection with space experiments, in cooperation with NASA and with the European Space Agency. Others relate to the joint Stanford-Lockheed Gravity-B experiment to use orbiting gyroscopes in a test of the general relativity theory and a Stanford experiment of the equivalence principle between gravitational and inertial mass. These studies will include reference calculations, but the underlying substance of the work will be mathematical. The formal theory is being developed from a completely rigorous point of view involving analysis of solutions of partial differential equations from a geometric perspective. The resulting experiments can be regarded as precise tests of the underlying physical hypotheses on which the mathematical formalism is based. The physical problems continue, in turn, to suggest new mathematical questions. ***