Schottky-Landau growth estimates for s-normal families of holomorphic mappings.
Schwarz Reflection Principle, Boundary Regularity and Compactness for -Complex Curves
We establish the Schwarz Reflection Principle for -complex discs attached to a real analytic -totally real submanifold of an almost complex manifold with real analytic . We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in -classes.
Schwarz-type lemmas for solutions of -inequalities and complete hyperbolicity of almost complex manifolds
The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.
Seiberg Witten invariants and uniformizations.
Seiberg-Witten invariants and pseudo-holomorphic subvarieties for self-dual, harmonic 2-forms.
Seifert n-Manifolds.
Semilinear equations, the function, and generalized Gauduchon metrics
In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the functions on the space of its hermitian metrics.
Serie de Poincaré-Koszul associée aux groupes de tresses pures.
Sharp bounds for the intersection of nodal lines with certain curves
Let be a hyperbolic surface and let be a Laplacian eigenfunction having eigenvalue with . Let be the set of nodal lines of . For a fixed analytic curve of finite length, we study the number of intersections between and in terms of . When is compact and a geodesic circle, or when has finite volume and is a closed horocycle, we prove that is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between and is . This bound is sharp.
Singular Moment Maps and Quaternionic Geometry
Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points
We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of GL(n, ℂ) is isomorphic to the deformation of the D2-singularity if n = 2, the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if n = 3, and to the Atiyah-Hitchin manifold itself if n = 4. For higher n, such slices to the sum of two orbits, each having only two distinct eigenvalues, are either empty or biholomorphic to open subsets of the Hilbert scheme of points on one of the above surfaces....
Smoothing q-convex functions and vanishing theorems.
Some characterizations of hyperbolic almost complex manifolds
First, we give some characterizations of the Kobayashi hyperbolicity of almost complex manifolds. Next, we show that a compact almost complex manifold is hyperbolic if and only if it has the Δ*-extension property. Finally, we investigate extension-convergence theorems for pseudoholomorphic maps with values in pseudoconvex domains.
Some geometry and combinatorics for the -invariant of ternary cubics.
Some remarks on a new pseudo-differential metric
Some remarks on the Casorati-Weierstrass theorem
Special Einstein’s equations on Kähler manifolds
This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov’s classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces.
Stabilité de la classe des variétés Kählériennes par certains morphismes propres.
Stability of the tangent bundle and existence of a Kähler-Einstein metric.
Stability of vector bundles and extremal metrics.