Mikhail Skopenkov (NRU HSE and IITP RAS)
Colloquium of the Department of Mathematics and Computer Science
Thursday November 26 at 18:15 zoom ID 958-115-833
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 process we reconstruct the positions of the cones for a given envelope. The methodology is based on the isotropic 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. The work was prepared within the framework of the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2018-2019 (grant N18-01-0023).
Everyone is welcome!