Speaker: M.B. Skopenkov (NRU Higher School of Economics, Institute for Information Transmission Problems RAS, Moscow, Russia).

Time: 2021-11-01 16:00 Novosibirsk time (12:00 Moscow time, 17:00 Beijing time).

Abstract: Motivated by applications in engineering, we provide characterizations of surfaces which are enveloped by a one-parametric family of congruent cones. As limit cases we also address developable surfaces and ruled surfaces. The characterizations are higher-order nonlinear PDEs generalizing the ones by Gauss and Monge. In the process we reconstruct the positions of the cones for a given envelope. The methodology is based on a model of Laguerre geometry, which transforms an envelope to a surface containing a special conic through each point. Most of the talk is explained in figures and is accessible to undergraduate students.

This is joint work with Pengbo Bo, Michael Barton, Helmut Pottmann.

Join Zoom Meeting
https://us06web.zoom.us/j/8243336174

Meeting ID: 824 333 6174