Download the PDF of the paper by Minju Lee and Hee Oh.

Download PDF

overview: Ratner’s orbit closure for the connected closed subgroup generated by the unipotent elements of $\operatorname{SO}(d,1)$ acting on the space $\Gamma\backslash \operatorname{SO}(d,1) We establish an analogue of the theorem. Suppose $, the associated hyperbolic manifold $M=\Gamma\backslash \mathbb H^d$ , is a convex cocompact manifold with a Fuchsian edge. For $d=3$ this was previously proved by McMullen, Mohammadi, and Oh. For higher dimensions, the possibility of accumulation in closed orbits of the intermediate group poses a very serious obstacle, and overcoming these by means of the avoidance theorem (Theorem 7.13) is the crux of this paper. Our result means that: for any $k\ge 1$ ,

(1) The closure of any $k$-holosphere in $M$ is a properly immersed submanifold.

(2) The closure of any geodesic $(k+1)$ plane in $M$ is a well-immersed submanifold.

(3) The infinite sequence of maximal well-embedded geodesic $(k+1)$ planes intersecting $\operatorname{core}M$ is dense at $M$.

Submission history

From: Hio [view email]


Mon 18 Feb 2019 15:46:42 UTC (579 KB)

Sun 24 Feb 2019 15:25:54 UTC (580 KB)

Tuesday, September 8, 2020 15:55:03 UTC (581 KB)

Tuesday, September 6, 2022 15:05:19 UTC (569 KB)

Saturday, March 25, 2023 15:44:23 UTC (685 KB)

Source link


Leave A Reply