9 citations · 26 across the 12 of their papers we have counts for
12 papers
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…
Bounded Geodesics on Locally Symmetric Spaces
Lifan Guan, Chengyang Wu
Let be a torsion-free subgroup of commensurable with , and be endowed with the natural locally symmetric space structure. We…
Boundary and Eisenstein Cohomology of
Jitendra Bajpai, Lifan Guan
In this article, Eisenstein cohomology of the arithmetic group with coefficients in any finite dimensional highest weight irreducible representation has been dete…
Dirichlet is not just Bad and Singular
Victor Beresnevich, Lifan Guan, Antoine Marnat +2
It is well known that in dimension one the set of Dirichlet improvable real numbers consists precisely of badly approximable and singular numbers. We show that in higher dimensions…
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…
Nondense orbits on homogeneous spaces and applications to geometry and number theory
Jinpeng An, Lifan Guan, Dmitry Kleinbock
Let be a Lie group, a discrete subgroup, , and an affine map from to itself. We give conditions on a submanifold of guaranteeing that the se…
Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents
Sam Chow, Anish Ghosh, Lifan Guan +2
We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting.…
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…
Bounded orbits of Diagonalizable Flows on finite volume quotients of products of
Jinpeng An, Anish Ghosh, Lifan Guan +1
We prove a number field analogue of W. M. Schmidt's conjecture on the intersection of weighted badly approximable vectors and use this to prove an instance of a conjecture of An, G…
Bounded orbits of certain diagonalizable flows on
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 .
Weighted badly approximable vectors and games
Lifan Guan, Jun Yu
We prove that the set of (r_1,r_2,..,r_{d})-badly approximable vectors is a winning set if r_1=r_2=...=r_{d-1}\geq r_{d}.
Bounded orbits of diagonalizable flows on
Jinpeng An, Lifan Guan, Dmitry Kleinbock
We prove that for any countably many one-parameter diagonalizable subgroups of , the set of such that…