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- W2763037810 abstract "We show that convex surfaces in an ambient three-sphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper S Superscript n plus 1> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>S</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>mathbb {S}^{n+1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature." @default.
- W2763037810 created "2017-10-20" @default.
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- W2763037810 date "2017-10-30" @default.
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- W2763037810 title "Curvature contraction flows in the sphere" @default.
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- W2763037810 doi "https://doi.org/10.1090/proc/13831" @default.
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