Lecture Event
Infinitesimal rigidity of convex surfaces and the Hilbert-Einstein functional
Dr. Ivan Izmestiev (TU Berlin)
5 Jan 2011, 15:15 – 16:45
Smooth strictly convex surfaces in R3 are infinitesimally rigid, i.e. they allow no non-trivial deformations that would preserve their intrinsic metric in the first order. We give a new proof of this which is based on variations of the Hilbert-Einstein functional.
Instead of deforming the surface, we reduce the question to "warped product"-deformations of the metric in the domain bounded by the surface. By studying the second variation of the Hilbert-Einstein functional, we show that every deformation that preserves the boundary metric and leaves the interior metric Euclidean must be trivial. This implies the infinitesimal rigidity of the surface.
Vortrag FS Differentialgeometrie:: http://geometrie.math.uni-potsdam.de/index.php/de/aktivitaeten/vortraege-fs-differentialgeometrie/343-infinitesimal-rigidity-of-convex-surfaces-and-the-hilbert-einstein-functional
Supported by