Mathematical Sciences: Numerical and Theoretical VariationalMethods in the Large and Applications to Geometry and       Topology
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{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
Jon Pitts will continue his study of minimal surfaces by                   variational techniques. This is an area which is currently                      experiencing dramatic developments. Pitts will focus his                        attention primarily on minimal surfaces in three dimensional                    manifolds rather than Euclidean space. The computational aspects                of this research provide a new direction for Pitts' research.                   This is an exciting development which is very much in line with                 contemporary work of other researchers.                                              The study of minimal surfaces in three dimensional manifolds               is an important aspect of Thurston's geometrization conjecture.                 Here the investigations will concern the possibility of                         constructing metrics which admit infinitely many minimal spheres                and tori. Another part of the project will be aimed at finding                  conditions on a noncompact hyperbolic manifold which guarantee                  that it supports a compact minimal surface. Pitts is also                       developing numerical methods for approximating minimal surfaces.                He will implement these algorithms in software and produce                      graphics of the stereographic images of the surfaces. The ability               to visualize these surfaces is rapidly becoming an essential                    ingredient of current research into these variational problems.
{'FirstName': 'Jon', 'LastName': 'Pitts', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jon Pitts', 'EmailAddress': 'j-pitts@tamu.edu', 'NSF_ID': '000373283', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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[{'Code': '126500', 'Text': 'GEOMETRIC ANALYSIS'}, {'Code': '127100', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
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