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Problems in the Geometry of Submanifolds John Douglas Moore

Summary: Problems in the Geometry of Submanifolds
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
e-mail: moore@math.ucsb.edu
This article grew out of several talks that the author presented at
the Banach Institute and at the University of Bialystok in Poland during
November of 2001. It describes six problems from the geometry of sub-
manifolds. Some of the problems come from the theory of constant cur-
vature submanifolds in Euclidean space, as well as applications of Morse
theory of the height function to the problem of relating curvature and
topology of submanifolds in Euclidean space. Others come from infinite-
dimensional Morse theory of minimal surfaces in Riemannian manifolds.
1 Introduction.
At the beginning of the new millennium, it was fashionable to present lists of
open problems within several specialties of mathematics.
A kind invitation from Professor Aminov to give a talk at the Banach Insti-
tute in Poland on "open problems in the geometry of submanifolds" gave the


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics