Mathematical Sciences:  Geometric Function Theory in SeveralComplex Variables
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{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Three main mathematical themes will be developed in this                   project, built around the theory of several complex variables.                  In the first, techniques from partial differential equations,                   especially real variable microlocal techniques, will be applied                 to provide insight into the relationship between the smoothness                 of a function and the type of curve (surface) which contains the                curve.  In one complex dimension one either concludes that the                  function must be smooth or else its Fourier coefficients decay                  slowly.  In higher dimensions this phenomenon is believed to be                 related to the nature of the wave front set.                                         Related work will involve questions of uniqueness for Cauchy               -Riemann functions.  Emphasis will be placed on the                             characterization of functions vanishing of infinite order along                 curves which are not complex tangential and on the relevance of                 the hypothesis of nonflatness as it relates to the regularity of                CR-mappings.                                                                         Additionally, work will be done on fundamental questions                   concerning holomorphic maps from complex n-dimensional space to                 itself.  Typical of these are maps whose Jacobian is unity having               images of finite volume (they exist) and automorphisms which, for               reasons unknown, do not distinguish countable dense sets, but act               differently on discrete countable sets.                                              This research will have application to the general                         understanding of the geometry of complex space and to complex                   partial differential operators defined on manifolds.
{'FirstName': 'Jean-Pierre', 'LastName': 'Rosay', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jean-Pierre Rosay', 'EmailAddress': 'jrosay@math.wisc.edu', 'NSF_ID': '000453027', 'StartDate': '05/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Wisconsin-Madison', 'CityName': 'MADISON', 'ZipCode': '537151218', 'PhoneNumber': '6082623822', 'StreetAddress': '21 North Park Street', 'StreetAddress2': 'Suite 6301', 'CountryName': 'United States', 'StateName': 'Wisconsin', 'StateCode': 'WI', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'WI02', 'ORG_DUNS_NUM': '161202122', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WISCONSIN SYSTEM', 'ORG_PRNT_DUNS_NUM': '041188822'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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