منابع مشابه
Harmonic Bergman Kernel for Some Balls
We treat the complex harmonic function on the Np–ball which is defined by the Np–norm related to the Lie norm. As a subspace, we treat Hardy spaces and consider the Bergman kernel on those spaces. Then, we try to construct the Bergman kernel in a concrete form in 2–dimensional Euclidean space. Introduction. In [2], [4], [6] and [7], we studied holomorphic functions and analytic functionals on t...
متن کاملOn the holomorphicity of proper harmonic maps between unit balls with the Bergman metrics
Let M and N be two Kähler manifolds with Kähler metrics h = hijdzidzj and g = gαβdwdwβ , respectively. Let u : M → N be a map from M to N . When both M and N are compact, in his proof of the celebrated strong rigidity theorem for compact Kähler manifolds, Siu [S1] proved that any harmonic map u must be holomorphic or antiholomorphic, under the assumption that N has strongly negative curvature i...
متن کاملI ) Introduction 1 to CR geometry and subelliptic harmonic maps . II ) Boundary values of Bergman - harmonic maps
We give an elementary introduction to CR and pseudohermitian geometry, starting from H. Lewy’s legacy (cf. [20]) i.e. tangential Cauchy-Riemann equations on the boundary of the Siegel domain. In this context we describe fundamental objects, such as contact structures, Levi forms, the Tanaka-Webster connection and the Fefferman metric (cf. e.g. [4]). Also naturally arising Hörmander systems of v...
متن کاملBergman Approximations of Harmonic Maps into the Space of Kähler Metrics on Toric Varieties
We generalize the results of Song-Zelditch on geodesics in spaces of Kähler metrics on toric varieties to harmonic maps of any compact Riemannian manifold with boundary into the space of Kähler metrics on a toric variety. We show that the harmonic map equation can always be solved and that such maps may be approximated in the C topology by harmonic maps into the spaces of Bergman metrics. In pa...
متن کاملOn proper harmonic maps between strictly pseudoconvex domains with Kähler metrics of Bergman type
where (h) is the inverse of the matrix (hij), ∆M = ∑ i,j h ∂ij and Γ s tγ denote the Christoffel symbols of the Hermitian metric g on N . It follows from (1.1) that if u is holomorphic, then u must be harmonic. Thus, it is natural to ask under what circumstances a harmonic map is holomorphic or antiholomorphic. Under the assumption that both M and N are compact, Siu [31] demonstrated that if th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2015
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201311_008