Uploaded November 2025 | Updated September 2026, 3 weeks ago
Scalar curvature encodA relation between the hyperspherical radius and Dirac eigenvalues will be used to give simple proofs of some classical rigidity results for scalar curvature. This includes Llarull's theorem, the Geroch conjecture and a recent inequality for fill-ins with nonnegtive scalar curvature. A new relation between the hyperspherical radius and the Yamabe invariant will be established. After that, the condition in Llarull's theorem that the comparison map has nonzero degree will be discussed.
Christian Bär (Potsdam)
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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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Scalar curvature encodA relation between the hyperspherical radius and Dirac eigenvalues will be used to give simple proofs of some classical rigidity results for scalar curvature. This includes Llarull's theorem, the Geroch conjecture and a recent inequality for fill-ins with nonnegtive scalar curvature. A new relation between the hyperspherical radius and the Yamabe invariant will be established. After that, the condition in Llarull's theorem that the comparison map has nonzero degree will be discussed.
Christian Bär (Potsdam)
===
Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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