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math.PR2026
On the Resistance Conjecture
Sylvester Eriksson-Bique
We give an affirmative answer to the resistance conjecture on characterization of parabolic Harnack inequalities in terms of volume doubling, upper capacity bounds and a Poincaré…
math.PR2025
On the energy image density conjecture of Bouleau and Hirsch
Sylvester Eriksson-Bique, Mathav Murugan
We affirmatively resolve the energy image density conjecture of Bouleau and Hirsch (1986). Beyond the original framework of Dirichlet structures, we establish the energy image dens…