Energy of generalized distributions

2015/12/04 by González-Dávila, J. C.
#53C12 #53C15 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C20 #Secundary 53C10

paper · doi:10.48550/arxiv.1512.01491

Abstract

We consider the energy of smooth generalized distributions and also of singular foliations on compact Riemannian manifolds for which the set of their singularities consists of a finite number of isolated points and of pairwise disjoint closed submanifolds. We derive a lower bound for the energy of all q-dimensional almost regular distributions, for each q< dim M, and find several examples of foliations which minimize the energy functional over certain sets of smooth generalized distributions.

Related

• Discrete and Continuous Green Energy on Compact Manifolds
• Energy estimates of harmonic maps between Riemannian manifolds
• Laplacians on generalized smooth distributions as C^*-algebra\n multipliers
• Lower bound for the Green energy of point configurations in harmonic manifolds
• Riemannian metrics and Laplacians for generalised smooth distributions