Hausdorff measure of the singular set of quasiregular maps on Carnot groups.
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
Hereditary orders, Gauss sums and supercuspidal representations of GLN.
High order regularity for subelliptic operators on Lie groups of polynomial growth.
Let G be a Lie group of polynomial volume growth, with Lie algebra g. Consider a second-order, right-invariant, subelliptic differential operator H on G, and the associated semigroup St = e-tH. We identify an ideal n' of g such that H satisfies global regularity estimates for spatial derivatives of all orders, when the derivatives are taken in the direction of n'. The regularity is expressed as L2 estimates for derivatives of the semigroup, and as Gaussian bounds for derivatives of the heat kernel....
Higher-dimensional algebra. V: 2-Groups.
Hilbert spaces for massless particles with nonvanishing helicities
Hilbert-Smith Conjecture for K - Quasiconformal Groups
MSC 2010: 30C60A more general version of Hilbert's fifth problem, called the Hilbert-Smith conjecture, asserts that among all locally compact topological groups only Lie groups can act effectively on finite-dimensional manifolds. We give a solution of the Hilbert-Smith Conjecture for K - quasiconformal groups acting on domains in the extended n - dimensional Euclidean space.
Hodge numbers and invariant complex structures of compact nilmanifolds
In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.
Hölder a priori estimates for second order tangential operators on CR manifolds
On a real hypersurface in of class we consider a local CR structure by choosing complex vector fields in the complex tangent space. Their real and imaginary parts span a -dimensional subspace of the real tangent space, which has dimension If the Levi matrix of is different from zero at every point, then we can generate the missing direction. Under this assumption we prove interior a priori estimates of Schauder type for solutions of a class of second order partial differential equations...
Holomorphic actions, Kummer examples, and Zimmer program
We classify compact Kähler manifolds of dimension on which acts a lattice of an almost simple real Lie group of rank . This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.
Holomorphic Anosov systems.
Holomorphic automorphisms and collective compactness in J*-algebras of operator
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball in a J*-algebra of operators. Let be the family of all collectively compact subsets W contained in . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when is a Cartan factor.
Holomorphic Discrete Series for the Real Symplectic Group.
Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. groups