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SUMMARY:Morse theory and rigidity for the Monge—Ampère equation - Andr
 è Guerra (University of Cambridge)
DTSTART:20251201T140000Z
DTEND:20251201T150000Z
UID:TALK240025@talks.cam.ac.uk
CONTACT:Zoe Wyatt
DESCRIPTION:I will begin by giving a brief overview of rigidity and flexib
 ility results in nonlinear PDE\, a prime example being the case of isometr
 ic embeddings. In two dimensions\, the rigidity/flexibility of isometric e
 mbeddings is closely related to rigidity/flexibility of non-convex solutio
 ns to the Monge-Ampère equation. I will then discuss a recent result\, ob
 tained with R. Tione\, which gives a complete rigidity result for solution
 s of the Monge-Ampère equation in general dimension\, as conjectured by 
 Šverák in 1992. The proof relies on Morse theory for non-smooth function
 s.
LOCATION:Lecture Room 2 in the gatehouse at INI
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