Mathematical Sciences: Some Problems in Geometric Analysis
{'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}
Paul Yang will work on three central problems in geometric                 analysis. The first of these involves investigating which                       functions on the sphere are Gaussian curvature functions of                     metrics conformally equivalent to the standard metric. The second               is to find out to what extent the universal cover of certain                    surfaces of negative curvature resembles the ball. In the final                 question the objective is to study the analytic and geometric                   nature of regions which give reliable data when used as sampling                regions.                                                                             The Nirenberg problem concerning characterizing Gaussian                   curvature functions is a delicate one in view of the necessary                  condition observed by Kazdan and Warner. Yang will focus his                    efforts on an investigation of functions admitting only two                     critical points. In the context of the uniformization problem                   Yang will investigate the conjecture that the universal cover of                a Kahler manifold of negative sectional curvature is                            biholomorphically equivalent to a bounded domain in complex                     n-space. The Pompieu problem will be reformulated in terms of the               existence of an infinite sequence of eigenfunctions to two dual                 systems of overdetermined boundary conditions.
{'FirstName': 'Paul', 'LastName': 'Yang', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Paul Yang', 'EmailAddress': 'yang@math.princeton.edu', 'NSF_ID': '000471112', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Southern California', 'CityName': 'LOS ANGELES', 'ZipCode': '90033', 'PhoneNumber': '2137407762', 'StreetAddress': '3720 S FLOWER ST FL 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '34', 'CONGRESS_DISTRICT_ORG': 'CA34', 'ORG_UEI_NUM': 'G88KLJR3KYT5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF SOUTHERN CALIFORNIA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126500', 'Text': 'GEOMETRIC ANALYSIS'}
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