Mathematical Sciences: Spectral Theory of Riemannian        Manifolds
{'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}
The principal investigator will study the eigenfunctions of                the Laplacian operator on complete Riemannian manifolds.  When                  the space is compact, he will provide upper and lower bounds for                the Hausdorff measure of the nodal set of these eigenfunctions.                 In the noncompact situation, he will derive lower bounds for the                decay of these eigenfunctions.                                                       Eigenfunctions of the Laplacian operator are the                           mathematical representations of harmonics of bells and musical                  instruments.  Peculiar shaped bells can have an intricate                       assortment of harmonics; often the third or seventh harmonics                   dominate.  In higher dimensions, the shapes of these bells are                  represented mathematically by Riemannian manifolds.  Were these                 bells to flare out to infinity, the Riemannian manifold would                   have to be noncompact. The principal investigator will study the                decay or damping out of such harmonics.
{'FirstName': 'Harold', 'LastName': 'Donnelly', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Harold Donnelly', 'EmailAddress': 'hgd@math.purdue.edu', 'NSF_ID': '000123916', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Purdue Research Foundation', 'CityName': 'WEST LAFAYETTE', 'ZipCode': '479064353', 'PhoneNumber': '3174946200', 'StreetAddress': '1281 WIN HENTSCHEL BLVD STE 2500', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'IN04', 'ORG_UEI_NUM': 'C1G1LGYJF5G5', 'ORG_LGL_BUS_NAME': 'PURDUE RESEARCH FOUNDATION', 'ORG_PRNT_UEI_NUM': 'YRXVL4JYCEF5'}
{'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=1989&All=true', 'xml': '8900219.xml'}