A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Theory for gravity coupled with fields on manifolds with null-boundary.
We consider a class of globally hyperbolic space-times with "expanding singularities". Under suitable assumptions we show that no -extensions across a compact boundary exist, while the boundary must be null wherever differentiable (which is almost everywhere) in the non-compact case.
Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.
The paper is concerned with regularity properties of boundaries of causal pasts of points in a 3+1-dimensional Einstein-vacuum spacetime. In a Lorentzian manifold such boundaries play crucial role in propagation of linear and nonlinear waves. We prove a uniform lower bound on the radius of injectivity of these null bou…
We investigate a problem posed by L. Hauswirth, F. Hélein, and F. Pacard, namely, to characterize all the domains in the plane that admit a "roof function", i.e., a positive harmonic function which solves simultaneously a Dirichlet problem with null boundary data, and a Neumann problem with constant boundary data. Unde…
This paper considers aspects of 4-manifold topology from the point of view of the null cone of a neutral metric, a point of view we call neutral causal topology. In particular, we construct and investigate neutral 4-manifolds with null boundaries that arise from canonical 3- and 4-dimensional settings. A null hypersurf…
Extends Penrose's method to null shells with pressure and energy flux.
New Markov chains defined on simplicial complexes for understanding their topology.