Mathematical Sciences: Stability Problems In The Theory Of Convex Sets

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Helmut Groemer will carry out research into stability problems associated with convex sets. Many theorems in the theory of convex sets state that under certain conditions a body is of an important special type or that two bodies are related to one another in a particular way. Corresponding to such results it is often easy to pose an associated stability problem. For example one might ask how close a body is to being a ball in terms of its isoperimetric deficit. The investigator has already made some progress in this direction notably in the case of results connected with projections of convex bodies. His future research will focus on stability problems associated with the Brunn-Minkowski theorem, symmetrization procedures, inscribed and circumscribed bodies. The anticipated techniques will involve geometric adaptations of spherical harmonics and Radon transforms.