scholarly journals An integral formula in Kähler geometry with applications

2016 ◽  
Vol 19 (05) ◽  
pp. 1650063 ◽  
Author(s):  
Xiaodong Wang
Keyword(s):  
Mean Curvature ◽  
Integral Formula ◽  
Kähler Manifold ◽  
Holomorphic Extension ◽  
Geometric Inequalities ◽  
Kahler Geometry ◽  
Cr Functions ◽  
Kahler Manifold ◽  
Extension Of Cr Functions

We establish an integral formula on a smooth, precompact domain in a Kähler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula, we also prove some geometric inequalities when the boundary has positive Hermitian mean curvature.

On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold

2016 ◽  
Vol 2016 (713) ◽  
Author(s):  
Tomoyuki Hisamoto
Keyword(s):  
Integral Formula ◽  
Kähler Manifold ◽  
Linear Series ◽  
Spectral Measures ◽  
Test Configuration ◽  
Kahler Manifold ◽  
The Family ◽  
Graded Linear Series

AbstractWe apply our integral formula of volumes to the family of graded linear series constructed from any test configuration. This solves the conjecture raised by Witt Nyström to the effect that the sequence of spectral measures for the induced ℂ

Separate holomorphic extension of CR functions

2009 ◽  
Vol 128 (4) ◽  
pp. 411-419
Author(s):  
Luca Baracco ◽  
Giuseppe Zampieri
Keyword(s):  
Holomorphic Extension ◽  
Cr Functions ◽  
Extension Of Cr Functions

Holomorphic extension of CR functions

1982 ◽  
Vol 49 (4) ◽  
pp. 757-784 ◽  
Author(s):  
Al Boggess ◽  
John C. Polking
Keyword(s):  
Holomorphic Extension ◽  
Cr Functions ◽  
Extension Of Cr Functions

scholarly journals CALIBRATIONS IN HYPER-KÄHLER GEOMETRY

2013 ◽  
Vol 15 (02) ◽  
pp. 1250060 ◽  
Author(s):  
GUEO GRANTCHAROV ◽  
MISHA VERBITSKY
Keyword(s):  
Kähler Manifold ◽  
Kahler Geometry ◽  
Kahler Manifold ◽  
Torsion Free

We describe a family of calibrations arising naturally on a hyper-Kähler manifold M. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When M is an HKT (hyper-Kähler with torsion) manifold with holonomy SL (n, ℍ), we construct another family of calibrations Φi, which calibrates holomorphic Lagrangian and holomorphic coisotropic subvarieties. The calibrations Φi are (generally speaking) not parallel with respect to any torsion-free connection on M.

Bergman metrics and geodesics in the space of Kähler metrics on principally polarized abelian varieties

2011 ◽  
Vol 11 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Renjie Feng
Keyword(s):  
Abelian Varieties ◽  
Kähler Manifold ◽  
Invariant Metrics ◽  
Kahler Geometry ◽  
Kähler Metrics ◽  
Complete Asymptotic Expansion ◽  
Kahler Metrics ◽  
Infinite Dimensional ◽  
Kahler Manifold ◽  
Bergman Metrics

AbstractIt is well known in Kähler geometry that the infinite-dimensional symmetric space $\mathcal{H}$ of smooth Kähler metrics in a fixed Kähler class on a polarized Kähler manifold is well approximated by finite-dimensional submanifolds $\mathcal{B}_k\subset\mathcal{H}$ of Bergman metrics of height k. Then it is natural to ask whether geodesics in $\mathcal{H}$ can be approximated by Bergman geodesics in $\mathcal{B}_k$. For any polarized Kähler manifold, the approximation is in the C0 topology. For some special varieties, one expects better convergence: Song and Zelditch proved the C2 convergence for the torus-invariant metrics over toric varieties. In this article, we show that some C∞ approximation exists as well as a complete asymptotic expansion for principally polarized abelian varieties.

scholarly journals Holomorphic extension of CR functions from quadratic cones

2009 ◽  
Vol 345 (2) ◽  
pp. 491-492
Author(s):  
Debraj Chakrabarti ◽  
Rasul Shafikov
Keyword(s):  
Holomorphic Extension ◽  
Cr Functions ◽  
Extension Of Cr Functions
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