Lifan Guan

activity

20162026

most citedDivergent trajectories on products of homogeneous spaces

2 citations · 2 across the 3 of their papers we have counts for

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6 papers · 1 filter

math.DS2026

Singular points for cone actions on the product of certain homogeneous spaces

Lifan Guan, Chengyang Wu

In this paper, we investigate divergent orbits for cone actions on products of certain homogeneous spaces. We introduce a notion of essential singularity for such actions, and esti…

math.DS2025

Bounded Geodesics on Locally Symmetric Spaces

Lifan Guan, Chengyang Wu

Let $Γ$ be a torsion-free subgroup of $S L_{3} (R)$ commensurable with $S L_{3} (Z)$ , and $Y = S O_{3} (R) \ S L_{3} (R) /Γ$ be endowed with the natural locally symmetric space structure. We…

math.DS2020★ 2 cited

Divergent trajectories on products of homogeneous spaces

Jinpeng An, Lifan Guan, Antoine Marnat +1

In this paper, we determine the Hausdorff dimension of the set of points with divergent trajectories on the product of certain homogeneous spaces. The flow is allowed to be weighte…

math.DS2020

Nondense orbits on homogeneous spaces and applications to geometry and number theory

Jinpeng An, Lifan Guan, Dmitry Kleinbock

Let $G$ be a Lie group, $Γ \subset G$ a discrete subgroup, $X = G /Γ$ , and $f$ an affine map from $X$ to itself. We give conditions on a submanifold $Z$ of $X$ guaranteeing that the se…

math.DS2018

Hausdorff dimension of divergent trajectories on homogeneous space

Lifan Guan, Ronggang Shi

For one parameter subgroup action on a finite volume homogeneous space, we consider the set of points admitting divergent on average trajectories. We show that the Hausdorff dimens…

math.DS2016

Bounded orbits of certain diagonalizable flows on $S L_{n} (R) / S L_{n} (Z)$

Lifan Guan, Weisheng Wu

We prove that the set of points that have bounded orbits under certain diagonalizable flows is a hyperplane absolute winning subset of $S L_{n} (R) / S L_{n} (Z)$ .