Mathematical Sciences: The Leviforms and CR Extension
{'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}
This project will continue work on problems of partial                     differential equations and geometric questions centering on the                 theory of several complex variables and complex geometry.                            Work will be done on restrictions of holomorphic functions                 to submanifolds.  These are functions which always satisfy                      certain equations known as the tangential Cauchy Riemann                        equations.  The investigations to be carried out on this project                involve the converse question:  What local geometric conditions                 on a submanifold of complex Euclidean space guarantee that each                 function satisfying the tangential Cauchy Riemann equations is                  locally the restriction of holomorphic function?  Methods of                    complex geometry and analysis will be applied in studying this                  fundamental question.  The geometric conditions are described by                curvature conditions as measured by the Levi forms and sector                   property conditions on the submanifold.  The analytic disc                      technique and the FBI transform will be used to construct the                   extension of a given CR function.                                                    Work will also be done in applying the technique of analytic               discs to prove Hardy Littlewood maximal function type estimates                 on domains in complex Euclidean space whose boundaries possess                  some weak form of convexity.  Results of this research are                      expected to have application to the theory of partial                           differential equations and to differential geometry.
{'FirstName': 'Albert', 'LastName': 'Boggess', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Albert Boggess', 'EmailAddress': 'boggess@asu.edu', 'NSF_ID': '000639951', 'StartDate': '07/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Texas A&M Research Foundation', 'CityName': 'COLLEGE STATION', 'ZipCode': '778454375', 'PhoneNumber': '9798626777', 'StreetAddress': '400 HARVEY MITCHELL PKWY S STE 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX', 'CONGRESSDISTRICT': '10', 'CONGRESS_DISTRICT_ORG': 'TX10', 'ORG_UEI_NUM': 'EQH8NQ4AXFT7', 'ORG_LGL_BUS_NAME': 'TEXAS A & M RESEARCH FOUNDATION', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
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