The global holomorphic invariant αG(M) introduced by Tian [6], Tian and Yau [5] is closely related to the existence of Kähler-Einstein metrics. In his solution of the Calabi conjecture, Yau [11] proved the existence of a KählerEinstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is posi...

Preface The book is devoted to the spectral theory of commutative C *-algebras of Toeplitz operators on Bergman spaces, and its applications. For each such commutative algebra we construct a unitary operator which reduces each Toeplitz operator from this algebra to a certain multiplication operator, thus also providing its spectral type representation. This gives us a powerful research tool all...

‎In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle‎. ‎We prove optimal estimates for the mapping properties of the Bergman projection on these domains.

The global holomorphic invariant αG(M) introduced by Tian[6], Tian and Yau[5] is closely related to the existence of Kähler-Einstein metrics. In his solution of the Calabi conjecture, Yau[11] proved the existence of a KählerEinstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is positiv...

The refined x-ray crystal structure of the phase Mg(27)Al(10.7(2))Zn(47.3(2)) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsu...

An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...

The canonical metric on a surface is of nonpositive curvature, so it is natural to study harmonic maps between canonical metrics on a surface in a fixed homotopy class. Through this approach, we establish the LBergman metric on Teichmüller space as the second variation of energy functionals of chosen families of harmonic maps.

A streamlined proof that the Bergman kernel associated to a quadrature domain in the plane must be algebraic will be given. A byproduct of the proof will be that the Bergman kernel is a rational function of z and one other explicit function known as the Schwarz function. Simplified proofs of several other well known facts about quadrature domains will fall out along the way. Finally, Bergman re...