Histoire de la réductibilité du groupe conforme des variétés riemanniennes (1964-1994)
Historický vývoj pojmu křivka [Book]
h-konvexe Kurven in der hyperbolischen Ebene.
Hochschild cohomology and deformations of Clifford-Weyl algebras.
Hochschild cohomology and quantization of Poisson structures
It is well-known that the question of existence of a star product on a Poisson manifold is open and only some partial results are known [see the author, J. Geom. Phys. 9, No. 1, 45-73 (1992; Zbl 0761.16012)].In the paper under review, the author proves the existence of the star products for the Poisson structures of the following type with , for some .
Hochschild cohomology theories in white noise analysis.
Hochschild homology and cohomology of Klein surfaces.
Hochshild cohomology and equivalence of graded star products.
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.
Hodge Spectral Sequence on Pseudoconvex Domains.
Hodge theory for twisted differentials
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds in class C of Fujiki, first stated by D. Arapura.
Hodge type decomposition
In the space of polynomial p-forms in ℝⁿ we introduce some special inner product. Let be the space of polynomial p-forms which are both closed and co-closed. We prove in a purely algebraic way that splits as the direct sum , where d* (resp. δ*) denotes the adjoint operator to d (resp. δ) with respect to that inner product.
Hodge-Bott-Chern decompositions of mixed type forms on foliated Kähler manifolds
The Bott-Chern cohomology groups and the Bott-Chern Laplacian on differential forms of mixed type on a compact foliated Kähler manifold are defined and studied. Also, a Hodge decomposition theorem of Bott-Chern type for differential forms of mixed type is proved. Finally, the case of projectivized tangent bundle of a complex Finsler manifold is discussed.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part I.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part II.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part II (Erratum).
Hofer’s metrics and boundary depth
We show that if is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer’s metric on the group of Hamiltonian diffeomorphisms of has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer’s metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in when satisfies...
Hofer-Zehnder capacity and length minimizing Hamiltonian paths.
Hofer–Zehnder capacity of unit disk cotangent bundles and the loop product
We prove a new finiteness result for the Hofer–Zehnder capacity of certain unit disk cotangent bundles. It is proved by a computation of the pair-of-pants product on Floer homology of cotangent bundles, combined with the theory of spectral invariants. The computation of the pair-of-pants product is reduced to a simple key computation of the Chas–Sullivan loop product.
Hölder continuous solutions to Monge–Ampère equations
Let be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on with right hand side, . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range of the complex Monge-Ampère operator acting on -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with -density belong to and proving that has the...