Semi-rigidity of horocycle flows over compact surfaces of variable negative curvature
نویسندگان
چکیده
منابع مشابه
On Mostow rigidity for variable negative curvature
We prove a finiteness theorem for the class of complete finite volume Riemannian manifolds with pinched negative sectional curvature, fixed fundamental group, and of dimension ≥ 3. One of the key ingredients is that the fundamental group of such a manifold does not admit a small nontrivial action on an R -tree.
متن کاملConformal Curvature Flows on Compact Manifold of Negative Yamabe Constant
Abstract. We study some conformal curvature flows related to prescribed curvature problems on a smooth compact Riemannian manifold (M, g0) with or without boundary, which is of negative (generalized) Yamabe constant, including scalar curvature flow and conformal mean curvature flow. Using such flows, we show that there exists a unique conformal metric of g0 such that its scalar curvature in the...
متن کاملThe Circle Problem on Surfaces of Variable Negative Curvature
In this note we study the problem of orbit counting for certain groups of isometries of simply connected surfaces with possibly variable negative curvature. We show that if N(t) denotes the orbit counting function for a convex co-compact group of isometries then for some constants C, h > 0, N(t) ∼ Ceht, as t→ +∞.
متن کاملRigidity in Non-negative Curvature
In this paper we will show that any complete manifold of nonnegative curvature has a flat soul provided it has curvature going to zero at infinity. We also show some similar results about manifolds with bounded curvature at infinity. To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compa...
متن کاملAdic Flows, Transversal Flows, and Horocycle Flows
We give a symbolic construction of Shunji Ito’s “transversal flow for a subshift of finite type” [I], along the lines of Vershik’s construction of an adic transformation. We then show how these flows arise naturally in the symbolic coding of horocycle flows on non-compact hyperbolic surfaces with finite area.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1987
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385700003801