13 citations · 15 across the 8 of their papers we have counts for
10 papers
The Calderón problem for harmonic spinors
Carlos Valero
We show that the conformal class of a compact spin manifold with boundary is uniquely determined by its boundary values of harmonic spinors if the metric is locally conformal to a…
A Uniqueness Result for the Calderon Problem for -connections coupled to spinors
Carlos Valero
In this paper we define a Dirichlet-to-Neumann map for a twisted Dirac Laplacian acting on bundle-valued spinors over a spin manifold. We show that this map is a pseudodifferential…
A Coordinate Free Formulation of Effective Diffusion on Channels
Carlos Valero
We study diffusion processes in regions generated by sliding a cross section by the phase flow of vector filed on curved spaces of arbitrary dimension. We do this by studying the e…
Anisotropy in 2D Discrete Exterior Calculus
Humberto Esqueda, Rafael Herrera, Salvador Botello +1
We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneit…
Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional Hyperbolic and de Sitter spaces
Carlos Valero, Raymond G. McLenaghan
We review the theory of orthogonal separation of variables on pseudo-Riemannian manifolds of constant non-zero curvature via concircular tensors and warped products. We then apply…
Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
Carlos Valero, Raymond G. McLenaghan
We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this…
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
Krishan Rajaratnam, Raymond G. McLenaghan, Carlos Valero
We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti.…
Singularities of the eigenvalue functions for first order symmetric symbols on rank two vector bundles over surfaces
Carlos Valero
For a rank two bundle over a surface , we study the set of singularities of the eigenvalue functions of symmetric symbols associated to first order differential op…
Maxwell's Equations, The Euler Index and Morse Theory
Carlos Valero
We show show that the singularities of the Fresnel surface for Maxwell's equation on an anisotrpic material can be accounted from purely topological considerations. The importance…
First Order Symbols on Surfaces and their multiplicity sets
Carlos Valero
We study the multiplicity sets of first order symbols associated with differential operators on two dimensional surfaces. This work is inspired by the phenomenon of conical refract…