Short self-contained proof of the quantitative isoperimetric inequality via quantitative calibrations that control asymmetry and excess.
A Selection Principle fo r the Sharp Quantitative Isoperimetric Inequality
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Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
Computer-assisted proof shows that the linearized operator around threefold symmetric traveling waves in the Burgers-Hilbert equation has an eigenvalue with negative real part for ω=3 and c≈1.1.
Derives relative energy inequality for compressible fluid around rotating body to prove weak-strong uniqueness and low Mach limit to incompressible rotating flow.
Stability with sharp exponent 2 holds for the L^p-Talenti inequality when f is the characteristic function of a subset of the unit ball.
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