Harmonic mappings of Kähler manifolds to locally symmetric spaces
Harmonic maps from surfaces to certain Kaehler manifolds.
Harmonic metrics on four dimensional non-reductive homogeneous manifolds
We study harmonic metrics with respect to the class of invariant metrics on non-reductive homogeneous four dimensional manifolds. In particular, we consider harmonic lifted metrics with respect to the Sasaki lifts, horizontal lifts and complete lifts of the metrics under study.
Harmonic -morphisms.
Harmonie Forms Dual to Geodesic Cycles in Quotients of SU (p, 1).
Harmonie Mappings and Kähler Manifolds.
Heat flows for extremal Kähler metrics
Let be a closed polarized complex manifold of Kähler type. Let be the maximal compact subgroup of the automorphism group of . On the space of Kähler metrics that are invariant under and represent the cohomology class , we define a flow equation whose critical points are the extremal metrics,i.e.those that minimize the square of the -norm of the scalar curvature. We prove that the dynamical system in this space of metrics defined by the said flow does not have periodic orbits, and that its...
Hermitian curvature flow
We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics...
Hermitian harmonic maps.
Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures
2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.
Hermitian Metrics of Negative Holomorphic Sectional Curvature on Some Hyperbolic Manifolds.
Hermitian natural tensors.
Hermitian spin surfaces with small eigenvalues of the Dolbeault operator
We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf surface. We give a complete classification of the ruled surfaces with this property. For the Hopf surfaces we obtain a partial classification and some examples
Hermitian surfaces of constant holomorphic sectional curvature.
Hidden symmetries of integrable systems in Yang-Mills theory and Kähler geometry
Hodge Spectral Sequence on Pseudoconvex Domains.
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.
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...
Holomorphic Affine and Projective Connections of Hyperbolic Type.
Holomorphic and Meromorphic Mappings and Curvature.