Mathematical Sciences: Applications of Analysis to Problems in Geometry
{'Code': '03040108', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'James Glazebrook'}
This research will focus on applications of analysis to                    problems in geometry. Jerry Kazdan will investigate continuation                properties of some elliptic operators. Christopher Croke will                   continue his work on geometric inequalities using techniques from               integral geometry. Dennis DeTurck will carry out research on the                curvature operator, the spectrum of the Laplacian and on                        existence theorems for some partial differential equations.                     Charles' Epstein's research in complex geometry will involve the                study of global biholomorphic invariants of Cauchy Riemann                      manifolds. They will be joined by Wenxiong Chen who will continue               his research into variational problems that arise in geometry.                       Kazdan's research is aimed at establishing uniqueness of                   continuation properties of elliptic operators which arise in                    geometric settings. This is to be modelled on known results about               harmonic functions where the corresponding operator is the                      Laplacian. Croke will investigate inequalities relating volume                  and injectivity radius. He will also study various associated                   stability results. DeTurck's research involves the study of                     nonlinear partial differential equations which arise in geometric               settings. These occur frequently when one prescribes various                    invariants of a physical system or tries to find those geometric                structures for which such invariants are optimal. Epstein's work                will include a study of the behavior of Kaehler-Einstein metrics                in the neighborhoods of simple singularities. The aim here is to                understand the effect of interior singularities on the values of                certain invariants.
[{'FirstName': 'Jerry', 'LastName': 'Kazdan', 'EmailAddress': 'kazdan@math.upenn.edu', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'Dennis', 'LastName': 'DeTurck', 'EmailAddress': 'deturck@math.upenn.edu', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Christopher', 'LastName': 'Croke', 'EmailAddress': 'ccroke@math.upenn.edu', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'University of Pennsylvania', 'CityName': 'Philadelphia', 'ZipCode': '191046205', 'PhoneNumber': '2158987293', 'StreetAddress': 'Research Services', 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA'}
[{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8722998.xml'}