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- W4379472327 abstract "Let $M$ be a closed hyperbolic manifold containing a totally geodesic hypersurface $S$, and let $N$ be a closed Riemannian manifold homotopy equivalent to $M$ with sectional curvature bounded above by $-1$. Then it follows from the work of Besson-Courtois-Gallot that $pi_1(S)$ can be represented by a hypersurface $S'$ in $N$ with volume less than or equal to that of $S$. We study the equality case: if $pi_1(S)$ cannot be represented by a hypersurface $S'$ in $N$ with volume strictly smaller than that of $S$, then must $N$ be isometric to $M$? We show that many such $S$ are rigid in the sense that the answer to this question is positive. On the other hand, we construct examples of $S$ for which the answer is negative." @default.
- W4379472327 created "2023-06-07" @default.
- W4379472327 creator A5059274626 @default.
- W4379472327 date "2023-06-01" @default.
- W4379472327 modified "2023-10-01" @default.
- W4379472327 title "Rigidity of Totally Geodesic Hypersurfaces in Negative Curvature" @default.
- W4379472327 doi "https://doi.org/10.48550/arxiv.2306.01254" @default.
- W4379472327 hasPublicationYear "2023" @default.
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