Mathematical Sciences: Isoperimetric Inequalities
{'Code': '03040108', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Trudy T. Sensibaugh'}
Erwin Lutwak will continue his investigations of the                       classical geometric inequalities. Attention will be focussed on                 establishing a theory dual to the Brunn-Minkowski theory. This                  latter theory has proved very powerful when applied to problems                 regarding projections of convex bodies. Lutwak's objective with                 the dual theory is to develop techniques applicable intersection                problems.                                                                            The Brunn-Minkowski theory of mixed volumes has in recent                  years been shown to have a dual theory applicable to starshaped                 sets. This arises essentially from use of the radial function                   rather than the support function of the set. Many of the                        classical results for projections and projection bodies have                    their duals in terms of intersections and intersection bodies.                  This duality is a useful tool in the study of the apparently                    anomalous behaviour of intersections.
{'FirstName': 'Erwin', 'LastName': 'Lutwak', 'EmailAddress': 'lutwak@nyu.edu', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Polytechnic University of New York', 'CityName': 'Brooklyn', 'ZipCode': '112013826', 'PhoneNumber': '7182603360', 'StreetAddress': '15 Metrotech Center', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY'}
{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8704474.xml'}