Optimal Transport: Stability and Monotonicity

Related lectures (32)

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Explains setting up experiments with compactness, isometries, and quasi-isometry.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Explores compact sets, extreme values, and function theorems on bounded sets.

Covers the fundamental group of a reattachment and surjection proofs with neighborhoods and cover overlays.

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.

Covers cell attachment, gluing cells, and separability in a compact space.

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Explores the properties of the quotient space X/G when X is compact and sometimes separated.