The relative extremal function for Borel sets in complex manifolds
英文摘要:
We study a disc formula for the relative extremal function for Borel sets in complex manifolds.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Armen Edigarian, Ragnar Sigurdsson
We study a disc formula for the relative extremal function for Borel sets in complex manifolds.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal homeomorphisms. On certain CR 3-manifolds, namely, CR circle bundles over flat tori, extremal quasiconformal homeomorphisms in some homotopy classes are constructed. These extremal mappings have similar behaviors to Teichmüller mappings on Riemann surfaces.
Characterization of continuity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds
研究紧致赫尔米特流形上极值函数连续性的局部性质,证明加权极值函数连续性依赖于极值函数和权重函数的连续性,推广Nguyen在紧致凯勒流形上的结果。
Hölder regularity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds
研究了紧致Hermitian流形上极值函数的Hölder连续性,证明其局部性质及加权极值函数的Hölder连续性,扩展了Nguyen在紧致Kähler流形上的结果。
An extremal quasiconformal homeomorphisms in a class of homeomorphisms between two CR 3-manifolds is an one which has the least conformal distortion among this class. This paper studies extremal quasiconformal homeomorphisms between CR 3-manifolds which admit transversal CR circle actions. Equivariant $K$-quasiconformal homeomorphisms are characterized by an area-preserving property and the $K$-quasiconformality of their quotient maps on the spaces of $S^1$-orbits. A large family of invariant CR structures on $S^3$ is constructed so that the extremal quasiconformal homeomorphisms among the equ…
We show that for a closed $n$-manifold $N$ admitting a quasiregular mapping from the Euclidean $n$-space the following are equivalent: (1) order of growth of $π_1(N)$ is $n$, (2) $N$ is aspherical, and (3) $π_1(N)$ is virtually $\mathbb{Z}^n$ and torsion free.
The main result of this paper is some "annulus" formula for the relative extremal function in the context of Stein spaces (Theorem 1.1). Our result may be useful in the theory of the extension of separately holomorphic functions on generalized (N,k)-crosses lying in the product of Stein manifolds (Theorem 4.6).
In joint work with Chen and Weber, the author has elsewhere shown that CP2#2(-CP2) admits an Einstein metric. The present paper gives a new and rather different proof of this fact. Our results include new existence theorems for extremal Kahler metrics, and these allow one to prove the above existence statement by deforming the Kahler-Einstein metric on CP2#3(-CP2) until bubbling-off occurs.
Through the study of the degenerate complex Monge-Ampère equation, we establish the optimal regularity of the extremal function associated to intrinsic norms of Chern-Levine-Nirenberg and Bedford-Taylor. We prove a conjecture of Chern-Levine-Nirenberg on the extended intrinsic norms on complex manifolds and verify Bedford-Taylor's representation formula for these norms in general.
Let M be a real analytic strictly pseudoconvex manifold of higher codimension in complex space, and let M' be the cartesian product of two or more compact real analytic strictly convex hypersurfaces. We prove that a germ of a biholomorphic map taking an open set in M to M' extends as a biholomorphic map along any path in M.
Regularity of the Siciak-Zaharjuta extremal function on compact Kähler manifolds
本文证明紧Kähler流形上极值函数的正则性为局部性质,将连续性与Hölder连续性等价于多重位势理论中的经典概念,并据此给出紧集$(\Cc^\al, \Cc^{\al'})$-正则性的有效刻画,证明$\bR^n$中所有紧的胖次解析子集均满足该正则性。
Balanced metrics for extremal Kähler metrics and Fano manifolds
本文先综述作者在代数几何平衡度量与稳定性概念方面的工作,再仅用Hopf--Rinow定理证明完备黎曼流形上测地凸函数临界点存在性的结论并推广至局部紧完备长度度量空间。
We show that a positive Borel measure of positive finite total mass, on compact Hermitian manifolds, admits a Holder continuous quasi-plurisubharmonic solution to the Monge-Ampere equation if and only if it is dominated locally by Monge-Ampere measures of Holder continuous plurisubharmonic functions.
We construct Koppelman formulas on manifolds of flags in $\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding $\debar$-equation. We also construct reproducing kernels for harmonic $(p,q)$-forms in the case of Grassmannians.
We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a notion of relative K-stability for Kähler manifolds, we prove that Kähler manifolds admitting extremal Kähler metrics are relatively K-stable. Along the way, we prove a general $L^p$ lower bound on the Calabi functional involving test configurations and their associated numerical invariants, answering a question of Donaldson. When the Kähler manifold is projective, our definition of relative K-stability is stronger than the usual definition given by Székelyhidi. In particular our result strengthens the k…
扫码添加微信好友,提出您的宝贵建议 👇
💡 备注请填写:网站反馈
发表机构由 AI 从论文文本抽取,如发现错误,欢迎反馈修正建议。