Large-scale conformal rigidity in dimension three

Quasi-conformal Rigidity of Negatively Curved Three Manifolds

In this paper we study the rigidity of infinite volume 3-manifolds with sectional curvature −b2 ≤ K ≤ −1 and finitely generated fundamental group. In-particular, we generalize the Sullivan’s quasiconformal rigidity for finitely generated fundamental group with empty dissipative set to negative variable curvature 3-manifolds. We also generalize the rigidity of Hamenstädt or more recently Besson-...

Conformal Anomaly and Large Scale Gravitational Coupling

We present a model in which the breackdown of conformal symmetry of a quantum stress-tensor due to the trace anomaly is related to a cosmological effect in a gravitational model. This is done by characterizing the traceless part of the quantum stress-tensor in terms of the stress-tensor of a conformal invariant classical scalar field. We introduce a conformal frame in which the anomalous trace ...

Geometric Rigidity of Conformal Matrices

We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace SO(n) by a arbitrary compact subset of conformal matrices, bounded away from 0 and invariant under SO(n), and rigid motions by Möbius transformations.

Rigidity and Inflexibility in Conformal Dynamics

Large-scale Rank and Rigidity of the Weil-petersson Metric

We study the large-scale geometry of Weil-Petersson space, that is, Teichmüller space equipped with the Weil-Petersson metric. We show that this admits a natural coarse median structure of a specific rank. Given that this is equal to the maximal dimension of a quasi-isometrically embedded euclidean space, we recover a result of Eskin Masur and Rafi which gives the coarse rank of the space. We g...