Mathematical Sciences: Complete Surfaces in Three-Space
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{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
Brian Smyth and Frederico Xavier will continue their work on               the theory of complete minimal surfaces. This is a subject where                great advances have taken place in the last decade. These were to               a large extent based on the conformal character of such surfaces.               In the current project attention will be focussed on more general               surfaces. Many of the important unresolved problems in this area                depend on an understanding of the analytic properties of the                    Gauss map. In particular it is important to investigate which                   meromorphic functions on the unit disc arise as Gauss maps of                   complete minimal surfaces.                                                           One of the principal motivations for this work arises from                 Efimov's result that any complete surface in three dimensional                  space which has negative Gauss curvature must have points where                 this curvature is arbitrarily close to zero. This in turn is                    related to the conjecture of Caratheodory that every compact                    surface in three dimensional space which has positive Gauss                     curvature must have at least two umbilic points. Smyth and Xavier               have already made substantial progress towards this conjecture                  and will continue their efforts in this direction. Other problems               which will be investigated include the question as to whether                   there are bounded non-compact complete surfaces with negative                   Gauss curvature.
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{'Name': 'University of Notre Dame', 'CityName': 'NOTRE DAME', 'ZipCode': '465565708', 'PhoneNumber': '5746317432', 'StreetAddress': '940 GRACE HALL', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'IN02', 'ORG_UEI_NUM': 'FPU6XGFXMBE9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF NOTRE DAME DU LAC', 'ORG_PRNT_UEI_NUM': 'FPU6XGFXMBE9'}
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{'Code': '126500', 'Text': 'GEOMETRIC ANALYSIS'}
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