Mathematical Sciences: Analytic and Geometric Function      Theory
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work on this project will concentrate on problems arising in            the theory of several complex variables, pluripotential theory,                 mapping properties in several variables, characteristic classes                 and with the rigidity of compact minimal surfaces in spheres.                           Investigations into the stability of solutions and the                  Dirichlet problem for the complex Monge-Ampere operator will be                 carried out.  These include determining the class of                            plurisubharmonic functions which make up the correct domain for                 this operator.  Stability questions center on the dependence of                 solutions on both boundary data and the inhomogenous part of the                operator.  The extent to which solutions converge when these                    related elements converge is still open.                                                Questions regarding mapping functions derive from earlier               results which show that high enough infinitesimal boundary                      contact of holomorphic maps forces the map to be biholomorphic.                 Work will be done on natural extensions of this work to find n-                 point Pick-Nevanlinna inequalities in several variables and to                  establish multivariate rigidity conditions on maps whose linear                 part is the identity.                                                                   Studies of minimal surfaces and surfaces of constant mean               curvature are necessarily linked to the understanding of harmonic               maps.  Recent work has shown that the set of conformal structures               of fixed topological type that can be realized as embedded                      minimal surfaces in the three-sphere is compact.  Minimally                     immersed surfaces are finite in number.  Work will be done in                   establishing whether or not this can be reduced to uniqueness.                          This research has application to nonlinear partial                      differential equations, differential geometry and higher                        dimensional potential theory.
[{'FirstName': 'B. Alan', 'LastName': 'Taylor', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'B. Alan Taylor', 'EmailAddress': 'taylor@umich.edu', 'NSF_ID': '000406324', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'Daniel', 'LastName': 'Burns', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': 'JR', 'PI_FULL_NAME': 'Daniel M Burns', 'EmailAddress': 'dburns@umich.edu', 'NSF_ID': '000177691', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'Regents of the University of Michigan - Ann Arbor', 'CityName': 'ANN ARBOR', 'ZipCode': '481091079', 'PhoneNumber': '7347636438', 'StreetAddress': '1109 GEDDES AVE, SUITE 3300', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Michigan', 'StateCode': 'MI', 'CONGRESSDISTRICT': '06', 'CONGRESS_DISTRICT_ORG': 'MI06', 'ORG_UEI_NUM': 'GNJ7BBP73WE9', 'ORG_LGL_BUS_NAME': 'REGENTS OF THE UNIVERSITY OF MICHIGAN', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8702365.xml'}