On Minimal Entropy and Stability |
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Authors: | Andrea Sambusetti |
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Institution: | (1) Institut Fourier de Mathématiques, Université de Grenoble I, BP 74, 38402 Saint Martin d'Hères, France |
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Abstract: | We study n-manifolds Y whose fundamental groups are subexponential extensions of the fundamental group of some closed locally symmetric manifold X of negative curvature. We show that, in this case, MinEnt(Y)n is an integral multiple of MinEnt(X)n, and the value MinEnt(Y) is generally not attained (unless if Y is diffeomorphic to X). This gives a new class of manifolds for which the minimal entropy problem is completely solved. Several examples (even complex projective), obtained by gluings and by taking plane intersections in complex projective space, are described. Some problems about topological stability, related to the minimal entropy problem, are also discussed. |
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Keywords: | entropy symmetric metric Kä hler– Einstein manifold |
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