Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space.
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...
Holes and obstacles
Holomorphe Differentialformen auf algebraischen Varietäten mit Singularitäten I.
Holomorphe Differentialformen zu Kongruenzgruppen der Siegelschen Modulgruppe.
Holomorphic curvature of infinite dimensional symmetric complex Banach manifolds of compact type.
Holomorphic extension maps for spaces of Whitney jets.
The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C∞-functions on an open subset of Rn. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of Rn into a space of holomorphic functions on an open subset D of Cn such that D ∩ Rn = RnF.
Holomorphic framings for projections in a Banach algebra.
Holomorphic mappings between spaces of different dimensions. II.
Holomorphic mappings between spaces of different dimensions. I.
Holomorphic maps of uniform type
Holomorphic Vector Fields with Simple Isolated Zeros.
Holonomicity in synthetic differential geometry of jet bundles.
Holonomy orbits of the snake charmer algorithm
Holonomy, twisting cochains and characteristic classes
This paper contains a description of various geometric constructions associated with fibre bundles, given in terms of important algebraic object, the “twisting cochain". Our examples include the Chern-Weil classes, the holonomy representation and the so-called cyclic Chern character of Bismut and others (see [2, 11, 27]), also called the Bismut’s class. The later example is the principal one for us, since we are motivated by the attempt to find an algebraic approach to the Witten’s index formula....
Homeotopy groups of punctured spheres with holes