Mathematical Sciences: Problems Related to Differential     Geometry and Mathematical Physics
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{'SignBlockName': 'Trudy T. Sensibaugh', 'PO_EMAI': None, 'PO_PHON': None}
Patricio Aviles will continue his work on partial                          differential equations connected with problems on differential                  geometry and mathematical physics. This work concerns four areas:               the Yamabe problem in complete Riemannian manifolds; liquid                     crystal problems; harmonic maps between two manifolds;                          singularities of positive solutions of semi-linear elliptic                     equations.                                                                           The compact Yamabe problem was solved by Schoen. Aviles will               try to extend his work with McOwen where they made some progress                in dealing with the case of complete manifolds. The liquid                      crystal work involves minimal surface theory and concerns an                    investigation of the size of singular sets of limiting                          configurations. The third topic focusses on the Dirichlet problem               for harmonic maps between complete manifolds of negative                        curvature. Interest in positive solutions of semi-linear elliptic               equations is motivated by study of the Yangs-Mills equations.                   Aviles is going to study non-isolated singularities.
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{'Name': 'University of Illinois at Urbana-Champaign', 'CityName': 'URBANA', 'ZipCode': '618013620', 'PhoneNumber': '2173332187', 'StreetAddress': '506 S WRIGHT ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '13', 'CONGRESS_DISTRICT_ORG': 'IL13', 'ORG_UEI_NUM': 'Y8CWNJRCNN91', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ILLINOIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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