E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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Date (published):
2022
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Event name:
Workshop on discrete geometric structures
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Event date:
29-Aug-2022 - 2-Sep-2022
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Event place:
Wien, Austria
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Keywords:
Mathematics Sciences
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Abstract:
It is a classical fact that the vertical component of an infinitesimal isometric deformation (IID) of a paraboloid of revolution is a harmonic function. In this talk we prove a discrete analog: the vertical component of an IID of a polyhedron inscribed in the paraboloid is a discrete harmonic function, with respect to the cotangent Laplacian. Similar, but less known is the fact that the radial component of an IID of a spherical domain is an eigenfunction of the spherical Laplacian. We establish a discrete analog: the radial component of an IID of an inscribed polyhedron is an eigenfunction of the discrete spherical Laplacian. The talk is based on a joint work with Roman Prosanov.
