3 papers
math.AP2025
Conjugate harmonic functions in 3D with respect to a unitary gradient
Pablo Pedregal
We propose to relax the classic Cauchy-Riemann equations for a mapping. We support the interest of such a proposal by looking at one specific situation in 3D, and proving the exist…
math.DG2024
Invariant Hulls and Geometric Variational Principles
Pablo Pedregal
We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameteri…
math.CA2024
Beyond Peano's theorem: a variational look at discontinuous ODE systems
Pablo Pedregal
We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Pea…