Introduces ℓ-convergence for Lorentzian pre-length spaces with stability of timelike curvature bounds, applies it to generalized cones for sharp bounds, and proves precompactness under uniform Ricci/Riemann bounds.
Lectures in Mathematics ETH Z¨ urich
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The paper reviews GHGF for HJ equations and proves a minimizing-movement construction for generalized characteristics plus that GHGF semi-flow invariant measures attaining c[H] are exactly the projected Mather measures.
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
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Convergence of Lorentzian spaces and curvature bounds for generalized cones
Introduces ℓ-convergence for Lorentzian pre-length spaces with stability of timelike curvature bounds, applies it to generalized cones for sharp bounds, and proves precompactness under uniform Ricci/Riemann bounds.