Mathematical Sciences: Geometric Variational Problems and   Related PDE Questions
{'Code': '03040108', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
Leon Simon and Brian White will study problems relating to                 regularity and singularity of minimal surfaces and extrema of                   other geometric variational problems.  Simon's research will                    proceed in three broad directions. The first of these involves                  problems relating to the singular set of minimal surfaces. The                  second concerns entire and exterior solutions of the minimal                    surface equation for the graph of a function. The final topic                   involves Willmore-type functionals.                                                  The basic questions regarding singular sets of minimal                     surfaces are concerned with the behaviour of such surfaces on                   approach to a singular point. Simon has already obtained strong                 results in the case where the singularity is isolated and will                  now investigate more general situations. The investigations of                  the minimal surface equation will center around the asymptotic                  behaviour of entire and exterior solutions. Here the emphasis                   will be on investigations in a high dimensional setting. The                    Willmore functional is a certain average of the mean curvature.                 The questions here relate to minimizing this functional over                    surfaces of a certain genus.                                                          White will investigate the dimension of the singular set of               area minimizing integral currents. This may lead to the discovery               of such sets of fractional dimension. A related problem is to                   find conditions under which almost every boundary gives rise to                 regular area minimizing disks. He will also investigate the                     existence of compact minimal submanifolds in Riemannian                         manifolds. One direction of research will involve an                            investigation of how many embedded minimal submanifolds exist.
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{'Name': 'Stanford University', 'CityName': 'STANFORD', 'ZipCode': '943052004', 'PhoneNumber': '6507232300', 'StreetAddress': '450 JANE STANFORD WAY', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '16', 'CONGRESS_DISTRICT_ORG': 'CA16', 'ORG_UEI_NUM': 'HJD6G4D6TJY5', 'ORG_LGL_BUS_NAME': 'THE LELAND STANFORD JUNIOR UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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