Mathematical Sciences: The Geometry of Image Surfaces of    Complex Functions
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff'}
This project will involve work on complex function theory                  using potential theory and Riemann surface methods.  The two                    areas of investigation are distinct but related.                                     First, work will be done on the geometry of image surfaces                 of analytic functions - particularly inner functions defined in                 a disc, and entire functions.  The research derives from older                  work of Gross on the structure of singularities of functions in                 the little Bloch space.  The methods involve the construction of                Riemann surfaces using Brownian  motion and potential theory.                        A second thrust will be made into problems of circle                       packings in the plane, motivated by a recent conjecture of                      Thurston.  It is now established that one may use circle                        packings to approximate classical conformal mappings.  An                       alternate approach to this theme will be pursued based on random                walks which are expected to provide a link between the graph and                approximations to Brownian motion.                                                   This work is expected to have application to numerical                     approximations to partial differential equations as well as to                  potential theory and probability.
{'FirstName': 'Kenneth', 'LastName': 'Stephenson', 'EmailAddress': 'KENS@MATH.UTK.EDU', 'StartDate': '08/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Tennessee Knoxville', 'CityName': 'Knoxville', 'ZipCode': '379163801', 'PhoneNumber': '8659743466', 'StreetAddress': '1331 CIR PARK DR', 'CountryName': 'United States', 'StateName': 'Tennessee', 'StateCode': 'TN'}
{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8702966.xml'}