Mathematical Sciences: Differential Geometry and Partial Differential Equations

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9504441 Schoen Several projects in the area of harmonic mappings and their applications, and the mathematical theory of general relativity are proposed. The proposer has recently investigated harmonic maps into non-locally compact spaces and found new applications of harmonic mapping theory. Schoen is also well-known for his proof with Yau of the positive mass conjecture in general relativity. One of the proposed problems is the so called Penrose conjecture which has to do with the mass of a space-time with a black hole, and the proposed research seeks a rigorous mathematical resolution of this conjecture.