Mathematical Sciences: Classical and Applied Analysis

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9400778 Finn 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. ***