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On a discretization of confocal quadrics: Geometric parametrizations, integrable systems and incircular nets

Abstract

Confocal quadrics lie at the heart of the system of confocal coordinates (also called elliptic coordinates). We suggest a geometric discretization which leads to factorisable discrete nets with a novel discrete analog of the orthogonality property and to an integrable discretization of the Euler-Poisson-Darboux equation. The coordinate functions of discrete confocal quadrics are computed explicitly. We demonstrate that special discrete confocal conics lead to incircular nets.

This is a joint work with W. Schief, Yu. Suris and J. Techter

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Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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