On a minimum principle in several complex variables
On a Monge-Ampère type equation in the Cegrell class
Let Ω be a bounded hyperconvex domain in ℂn and let μ be a positive and finite measure which vanishes on all pluripolar subsets of Ω. We prove that for every continuous and strictly increasing function χ:(-∞,0) → (-∞,0) there exists a negative plurisubharmonic function u which solves the Monge-Ampère type equation . Under some additional assumption the solution u is uniquely determined.
On a Natural Algebraic Affine Connection on the Space of Almost Complex Structures and the Curvature of Teichmüller Space with Respect to its Weil-Petersson Metric.
On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball.
On a partial complex structure
On a Problem Concerning the Intrinsic Characterization of Cn.
On a Purely ?Riemannian" Proof of the Structure and Dimension of the Unramified Moduli Space of a Compact Riemann Surface.
On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions...
On a subvariety of the moduli space.
We give an explicit description of a non-normal irreducible subvariety of the moduli space of Riemann surfaces of genus 3 characterized by a non-cyclic group action. Defining equations of a family of curves representing non-normal points of this subvariety are computed. We also find defining equations of the family of hyperelliptic curves of genus 3 whose full automorphism group is C2 X C4. This completes the list of full automorphism groups of hyperelliptic curves.
On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates
Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.
On a theorem of Kontsevich.
On a two-variable zeta function for number fields
This paper studies a two-variable zeta function attached to an algebraic number field , introduced by van der Geer and Schoof, which is based on an analogue of the Riemann-Roch theorem for number fields using Arakelov divisors. When this function becomes the completed Dedekind zeta function of the field . The function is a meromorphic function of two complex variables with polar divisor , and it satisfies the functional equation . We consider the special case , where for this function...
On a volume element of a Hitchin component
Let Σ be a closed oriented Riemann surface of genus at least 2. By using symplectic chain complex, we construct a volume element for a Hitchin component of Hom(π₁(Σ),PSLₙ(ℝ))/PSLₙ(ℝ) for n > 2.
On abelian subvarieties generated by symmetric correspondences.
On actions of on algebraic spaces
The main result of the paper says that all schematic points of the source of an action of on an algebraic space are schematic on .
On algebraic curves.
On algebraic curves (of low genus) defined by Kleinian groups
On Algebraicity of Global Real Analytic Sets and Functions
On an Estimate of Axler and Shapiro.
On an integral formula of Berndtsson related to the inversion of the Fourier-Laplace transform of -closed -forms
We give a proof of an integral formula of Berndtsson which is related to the inversion of Fourier-Laplace transforms of -closed -forms in the complement of a compact convex set in .