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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Geometry and Topology Seminar: Regularity of the moduli space of parallel ovaloids

Presented by Wilhelm Klingenberg, Durham University

9 February 2017 13:00 in CM221

An ovaloid is a closed, unparametrized surface of positive curvature in Euclidean 3 - space. The collection \S of *all* C^{2,a}-regular ovaloids is equipped with a natural submanifold topology. Then \S admits Euclidean motions, and, less trivially, parallelism (resulting from pairs of ovaloids of constant ambient distance), where both act continuously on \S. In this talk we consider the quotient space \L := \S modulo parallelism, which inherits the quotient topology from \S. We then report a result, obtained jointly with B. Guilfoyle, that details a regularity property of the topological space \L. This is proved using the extrinsic geometry of ovaloids, namely properties of the principal curvature foliation that are invariant under parallelism, and thereby descend to \L. Our talk will be self-contained, and in particular we will develop the required elements of classical differential geometry in an elementary and conceptual way.

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