Mathematical Sciences: Geometric Methods in the Theory of   Functions
{'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}
In this project work will be done on self-conformal mappings            of Riemann surfaces.  In recent work the principal investigator                 has given a representation for arbitrary Riemann surfaces which                 provided simple proofs of old results together with new                         applications to self-conformal maps of surfaces which have a                    fixed point.  In cases where the group of maps have several base                points good progress has been made in describing the groups in                  terms of congruent polygons.                                                            Related to this work is on-going research measuring the                 number of regular mappings between a fixed (closed) Riemann                     surface to surfaces of lower genus.  This finite bound depends                  only on the genus of the original surface.  Similar questions                   regarding maps between multiply connected plane domains will be                 treated.                                                                                The extremal metric method and Loewner's variational method             of studying univalent functions have never been studied for                     connections.  A careful analysis of this question will be                       undertaken.  Aside from general interest, the outcome of this                   effort should provide a characterization of Loewner chains                      associated with quadratic differentials.
{'FirstName': 'James', 'LastName': 'Jenkins', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'James A Jenkins', 'EmailAddress': 'lucy@math.wustl.edu', 'NSF_ID': '000233031', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Washington University', 'CityName': 'SAINT LOUIS', 'ZipCode': '63110', 'PhoneNumber': '3147474134', 'StreetAddress': 'ONE BROOKINGS DR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Missouri', 'StateCode': 'MO', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'MO01', 'ORG_UEI_NUM': 'L6NFUM28LQM5', 'ORG_LGL_BUS_NAME': 'WASHINGTON UNIVERSITY, THE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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