Globally invertible differentiable or holomorphic maps
Graphs of finite mass which annot be approximated in area by smooth graphs.
H¹ and BMO for certain locally doubling metric measure spaces of finite measure
In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class...
Hamiltonien périodique de surface : désintégration de Floquet
Handle attaching in symplectic homology and the Chord Conjecture
Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a haracteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant . More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords. The proof relies...
Hard implicit function theorem and small periodic solutions to partial differential equations
Harmonic Maps of the Moduli Space of Compact Riemann Surfaces.
Harmonic morphisms onto Riemann surfaces and generalized analytic functions
We study harmonic morphisms from domains in and to a Riemann surface , obtaining the classification of such in terms of holomorphic mappings from a covering space of into certain Grassmannians. We show that the only non-constant submersive harmonic morphism defined on the whole of to a Riemann surface is essentially the Hopf map.Comparison is made with the theory of analytic functions. In particular we consider multiple-valued harmonic morphisms defined on domains in and show how a cutting...
Harmonicity of horizontally conformal maps and spectrum of the Laplacian.
Harmonie Mappings and Kähler Manifolds.
Hausdorff measures and the Morse-Sard theorem.
Let F : U ⊂ Rn → Rm be a differentiable function and p < m an integer. If k ≥ 1 is an integer, α ∈ [0, 1] and F ∈ Ck+(α), if we set Cp(F) = {x ∈ U | rank(Df(x)) ≤ p} then the Hausdorff measure of dimension (p + (n-p)/(k+α)) of F(Cp(F)) is zero.
Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper Kähler morphisms.
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 mappings between spaces of different dimensions. II.
Holomorphic mappings between spaces of different dimensions. I.
Holomorphic maps of uniform type
Homomorphism between Homotopy groups induced by elements of the sobolev space L1, p (M, N).
Homöomorphieaussagen für -verdichtende Vektorfelder
Homotopien von Untermannigfaltigkeiten mit nicht ausgearteter zweiter Fundamentalform
Homotopy classification of regular sections