23 citations · 41 across the 7 of their papers we have counts for
8 papers
Invariance of intrinsic hypercontractivity under perturbation of Schrödinger operators
Leonard Gross
A Schrödinger operator that is bounded below and has a unique positive ground state can be transformed into a Dirichlet form operator by the ground state transformation. If the res…
Equivalence of helicity and Euclidean self-duality for gauge fields
Leonard Gross
In the canonical formalism for the free electromagnetic field a solution to Maxwell's equations is customarily identified with its initial gauge potential (in Coulomb gauge) and in…
Stability of the Yang-Mills heat equation for finite action
Leonard Gross
The existence and uniqueness of solutions to the Yang-Mills heat equation over domains in Euclidean three space was proven in a previous paper for initial data lying in the Sobolev…
Initial behavior of solutions to the Yang-Mills heat equation
Nelia Charalambous, Leonard Gross
We explore the small-time behavior of solutions to the Yang-Mills heat equation with rough initial data. We consider solutions with initial value , where…
The Yang-Mills heat equation with finite action
Leonard Gross
The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over three dimensional Euclidean space and over a bounded open convex set therein. The initial d…
Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
Nathaniel Eldredge, Leonard Gross, Laurent Saloff-Coste
We show that for a hypoelliptic Dirichlet form operator A on a stratified complex Lie group, if the logarithmic Sobolev inequality holds, then a holomorphic projection of A is stro…
Neumann domination for the Yang-Mills heat equation
Nelia Charalambous, Leonard Gross
Long time existence and uniqueness of solutions to the Yang-Mills heat equation have been proven over a compact 3-manifold with boundary for initial data of finite energy. In the p…
The Yang-Mills heat semigroup on three-manifolds with boundary
Nelia Charalambous, Leonard Gross
Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie alge…