6 citations · 10 across the 8 of their papers we have counts for
8 papers
Derivatives of Sub-Riemannian Geodesics are -Hölder Continuous
Lev Lokutsievskiy, Mikhail Zelikin
This article is devoted to the long-standing problem on the smoothness of sub-Riemannian geodesics. We prove that the derivatives of sub-Riemannian geodesics are always -Hölde…
Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies and the limiting case of infinite height
Lev Lokutsievskiy, Gerd Wachsmuth, Mikhail Zelikin
We consider Newton's problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions an…
The analytical solution to Newton's aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary
L. V. Lokutsievskiy, M. I. Zelikin
The method of Hessian measures is used to find the differential equation that defines the optimal shape of nonrotationally symmetric bodies with minimal resistance moving in a rare…
Hessian measures in the aerodynamic Newton problem
L. V. Lokutsievskiy, M. I. Zelikin
Simple natural proofs of all known results regarding the aerodynamic Newton problem are obtained. Additional new theorems and new promising formulas in terms of Hessian measures ar…
The fractal theory of the Saturn Ring
Mikhail Zelikin
The true reason for partition of the Saturn ring as well as rings of other planets into great many of sub-rings is found. This reason is the theorem of Zelikin-Lokutsievskiy-Hildeb…
Field Theory for Multiple Integrals
M. Zelikin
New constructions in the theory of fields for multiple integrals are designed. Generalizations of the Legendre - Weyl - Caratheodory transforms and corresponding invariant integral…
Quantized geodesic flow and superconductivity of plasma in fireballs
M. Zelikin
An explanation of stability of fireballs is proposed based on quantum effects in a thin surface layer of negatively charged plasma surrounding a positive kernel of a fireball. We c…
Geometry of cross ratio
M. I. Zelikin
Generalization of the cross ratio to polarizations of linear finite and infinite-dimensional spaces (in particular to Sato Grassmannian) is given and explored. This cross ratio app…