Rigidity of amalgamated products in negative curvature

G´erard Besson Institut Fourier Gilles Courtois Ecole Polytechnique Sylvain Gallot Institut Fourier

Differential Geometry mathscidoc:1609.10072

Journal of Differential Geometry, 79, (3), 335-387, 2008
Let .. be the fundamental group of a compact riemannian manifold X of sectional curvature K ≤ .1 and dimension n ≥ 3. We suppose that .. = A .C B is the free product of its subgroups A and B amalgamated over the subgroup C. We prove that the critical exponent δ(C) of C satisfies δ(C) ≥ n.2. The equality occurs if and only if there exist an embedded compact hypersurface Y . X, totally geodesic, of constant sectional curvature .1, whose fundamental group is C and which separates X in two connected components whose fundamental groups are A and B respectively. Similar results hold if .. is an HNN extension, or more generally if .. acts on a simplicial tree without fixed point.
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@inproceedings{g´erard2008rigidity,
  title={RIGIDITY OF AMALGAMATED PRODUCTS IN NEGATIVE CURVATURE},
  author={G´erard Besson, Gilles Courtois, and Sylvain Gallot},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909132658438275729},
  booktitle={Journal of Differential Geometry},
  volume={79},
  number={3},
  pages={335-387},
  year={2008},
}
G´erard Besson, Gilles Courtois, and Sylvain Gallot. RIGIDITY OF AMALGAMATED PRODUCTS IN NEGATIVE CURVATURE. 2008. Vol. 79. In Journal of Differential Geometry. pp.335-387. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909132658438275729.
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