Weak Forms of the Ehrenpreis Conjecture and the Surface Subgroup Conjecture
نویسنده
چکیده
We prove the following: 1. Let ǫ > 0 and let S1, S2 be two closed hyperbolic surfaces. Then there exists locallyisometric covers S̃i of Si (for i = 1, 2) such that there is a (1 + ǫ) bi-Lipschitz homeomorphism between S̃1 and S̃2 and both covers S̃i (i = 1, 2) have bounded injectivity radius. 2. Let M be a closed hyperbolic 3-manifold. Then there exists a map j : S → M where S is a surface of bounded injectivity radius and j is π1-injective local isometry onto its image. MSC: 20E07, 57M10, 57M50
منابع مشابه
Proof of the Ehrenpreis Conjecture and the Surface Subgroup Conjecture
We prove the following two conjectures. 1. (The Ehrenpreis Conjecture) Let ǫ > 0 and let S1, S2 be two closed Riemann surfaces of the same genus. Then there exists finite covers S̃i of Si (for i = 1, 2) such that there is a (1 + ǫ)-quasiconformal homeomorphism between S̃1 and S̃2. 2. (The Surface Subgroup Conjecture) Let M be a closed hyperbolic 3-manifold. Then there exists a subgroup G < π1(M) s...
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