Bounded Earthquakes

Some remarks on bounded earthquakes

We first show that an earthquake of a geometrically infinite hyperbolic surface induces an asymptotically conformal change in the hyperbolic metric if and only if the measured lamination associated with the earthquake is asymptotically trivial on the surface. Then we show that the contraction along earthquake paths is continuous in the Teichmüller space of any hyperbolic surface. Finally, we show that if a measured lamination vanishes while approaching infinity at the rate higher than the distance to the boundary then it must be trivial.

全纯等距映射从复单位球到有界对称域的逐分量刚性

Componentwise rigidity of holomorphic isometric maps between bounded symmetric domains with negative conformal factors

本文证明了从复单位球到不可约有界对称域乘积的全纯等距映射的每个非常数分量本身也是全纯等距（相差常数因子），从而解决了 Yuan 于 2019 年提出的逐分量刚性猜想。

A characterization of varieties whose universal cover is a bounded symmetric domain without ball factors

We give two characterizations of varieties whose universal cover is a bounded symmetric domain without ball factors in terms of the existence of a holomorphic endomorphism \s of the tensor product T\otimes T' of the tangent bundle T with the cotangent bundle T'. To such a curvature type tensor \s one associates the first Mok characteristic cone S, obtained by projecting on T the intersection of ker (\s) with the space of rank 1 tensors. The simpler characterization requires that the projective scheme associated to S be a finite union of projective varieties of given dimensions and codimensions…