Harmonic induction on Lie groups.
Harmonic maps and representations of non-uniform lattices of
We study representations of lattices of into . We show that if a representation is reductive and if is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic -space to complex hyperbolic -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into of non-uniform lattices in , and more generally of fundamental groups of orientable...
Harmonic maps into singular spaces and -adic superrigidity for lattices in groups of rank one
Harmonic properties of the sum-of-digits function for complex bases
Harmonically Induced Representations of Nilpotent Lie Groups.
Harmonische Analyse auf gewissen nilpotenten Lieschen Gruppen
Hausdorff dimensions of limit sets I.
Hausdorff measure of the singular set of quasiregular maps on Carnot groups.
Hausdorff topologies on the a-bicyclic semigroup.
Hausdorff-Maße von Summenmengen. I.
Hausdorff-Maße von Summenmengen. II:
H-Coextensions in the category of compact semigroups.
Heat kernel and semigroup estimates for sublaplacians with drift on Lie groups.
Let G be a Lie group. The main new result of this paper is an estimate in L2 (G) for the Davies perturbation of the semigroup generated by a centered sublaplacian H on G. When G is amenable, such estimates hold only for sublaplacians which are centered. Our semigroup estimate enables us to give new proofs of Gaussian heat kernel estimates established by Varopoulos on amenable Lie groups and by Alexopoulos on Lie groups of polynomial growth.
Heat kernel estimates for a class of higher order operators on Lie groups
Let G be a Lie group of polynomial volume growth. Consider a differential operator H of order 2m on G which is a sum of even powers of a generating list of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list which is sufficient to ensure that the semigroup kernel of H satisfies global Gaussian estimates for all times. For G not necessarily solvable, we state an analytic condition on the list which is necessary and sufficient for global Gaussian estimates....
Heat kernel measure on central extension of current groups in any dimension.
Heat kernel transform for nilmanifolds associated to the Heisenberg group.
Heat kernels and Riesz transforms on nilpotent Lie groups
We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian lower bounds...
Hecke operators on quasimaps into horospherical varieties.
Hecke theory for
Hereditarily unicoherent continua and monotone structures.