Mathematical Sciences: Constant Mean Curvature Surfaces /   Isoparametric Spectral Geometry
{'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}
Bruce Solomon will carry out research in two fairly                        independent projects, although the techniques to be employed will               be similar in both cases. The first is the study of constant mean               curvature surfaces. Most work here has been done on minimal                     surfaces, the case of zero curvature. In recent years the work of               Wente has stimulated interest in the case of non-zero curvature.                This arose from Wente's construction of a counterexample to                     Hopf's long standing conjecture that all soap bubbles are                       spheres. It is now becoming clear that there is a rich theory of                these surfaces analogous but different from that of minimal                     surfaces. The second area involves the study of isoparametric                   surfaces. These have the property that the distinct principal                   curvatures at each point are the same. Interest in such surfaces                stems from the fact that they behave in a fashion very similar to               the homogeneous spaces. Solomon will focus his attention on the                 spectral theory of isoparametric minimal surfaces in spheres.                        The first topic will involve an investigation of the moduli                space of complete constant mean curvature surfaces. The intention               here is to compare and contrast this theory with that of minimal                surfaces. The study of spectral properties of isoparametric                     surfaces is important since they are in many ways the natural                   successors to the symmetric spaces and they provide the only                    other setting in which the spectrum of the Laplace operator is                  known. The eigenvalues are in fact integers and so it is natural                to investigate the geometric consequences of such an observation.               The key to the study of these surfaces is the fact that they                    decompose into mutually orthogonal geodesic foliations by                       subspheres of the ambient sphere.
{'FirstName': 'Bruce', 'LastName': 'Solomon', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Bruce Solomon', 'EmailAddress': 'solomon@indiana.edu', 'NSF_ID': '000460080', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Indiana University', 'CityName': 'BLOOMINGTON', 'ZipCode': '474057000', 'PhoneNumber': '3172783473', 'StreetAddress': '107 S INDIANA AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '09', 'CONGRESS_DISTRICT_ORG': 'IN09', 'ORG_UEI_NUM': 'YH86RTW2YVJ4', 'ORG_LGL_BUS_NAME': 'TRUSTEES OF INDIANA UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'YH86RTW2YVJ4'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8800414.xml'}