For p>1, the relative p-Faber-Krahn inequality is shown to be equivalent to volume doubling together with a sub-Gaussian upper estimate for Trudinger subsolutions, with improved long-time bounds under uniform Faber-Krahn decay.
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Relative Faber--Krahn inequalities and Trudinger's equation on Riemannian Manifolds
For p>1, the relative p-Faber-Krahn inequality is shown to be equivalent to volume doubling together with a sub-Gaussian upper estimate for Trudinger subsolutions, with improved long-time bounds under uniform Faber-Krahn decay.