Tags » Math.DG
Last time, we showed the first part of Burns-Masur-Wilkinson ergodicity criterion:
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Theorem 1 (Burns-Masur-Wilkinson) Let be the quotient of a contractible, negatively curved, possibly incomplete, Riemannian manifold by a subgroup of isometries of acting freely and properly discontinuously.
Last time, we reduced the proof of Burns-Masur-Wilkinson theorem on the ergodicity (and mixing) of the Weil-Petersson geodesic flow to a certain estimate for the first derivative of a geodesic flow on negatively curved manifolds (cf. 4,041 more words
Let be an irreducible polynomial in three variables. As is not algebraically closed, the zero set can split into various components of dimension between and . 1,307 more words
Today we will define the Weil-Petersson (WP) metric on the cotangent bundle of the moduli spaces of curves and, after that, we will see that the WP metric satisfies the first three items of the… 5,688 more words