Extended Monge-Kantorovich Theory

Abstract

Abstract: 1 Abstract 2 Generalized geodesics and the Monge-Kantorovich theory 2.1 Generalized geodesics 2.2 Extension to probability measures 2.3 A decomposition result 2.4 Relativistic MKT 2.5 A relativistic heat equation 2.6 Laplace s equation and Moser s lemma revisited 3 Generalized Harmonic functions 3.1 Classical harmonic functions 3.2 Open problems 4 Multiphasic MKT 5 Generalized extremal surfaces 5.1 MKT revisited as a subset of generalized surface theory 5.2 Degenerate quadratic cost functions 6 Generalized extremal surfaces in and Electrodynamics 6.1 Recovery of the Maxwell equations 6.2 Derivation of a set of nonlinear Maxwell equations 6.3 An Euler-Maxwell-type system References