Bartnik Hilbert manifold structure on fibers of the scalar curvature and the constraint operator

Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

We provide a Hilbert manifold structure {à} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{é} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.

Hilbert Manifold Structure of The Set of Solutions of Constraint Equations For Coupled Einstein and Scalar Fields

In this paper, we prove that the set of solutions of constraint equations for coupled Einstein and scalar fields in classical general relativity possesses Hilbert manifold structure. We follow the work of R. Bartnik [2] and use weighted Sobolev spaces and Implicit Function Theorem to prove our results.

A construction of hyperkähler metrics through Riemann-Hilbert problems I

In 2009 Gaiotto, Moore and Neitzke presented a new construction of hyperkähler metrics on the total spaces of certain complex integrable systems, represented as a torus fibration $\mathcal{M}$ over a base space $\mathcal{B}$, except for a divisor $D$ in $\mathcal{B}$, in which the torus fiber degenerates into a nodal torus. The hyperkähler metric $g$ is obtained via solutions $\mathcal{X}_γ$ of a Riemann-Hilbert problem. We interpret the Kontsevich-Soibelman Wall Crossing Formula as an isomonodromic deformation of a family of RH problems, therefore guaranteeing continuity of $\mathcal{X}_γ$ at…

Direct Images and Hilbert Fields

In this article we undertake a careful study of the curvature operator of a field of Bergman spaces associated to a holomorphic fibration of Kähler manifolds. We focus on the case when the fibers are smoothly bounded pseudoconvex domains.

伪芬斯勒几何中的爱因斯坦-希尔伯特-帕拉蒂尼形式

The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry

本文系统发展了任意符号伪芬斯勒度量的Palatini形式体系，通过引入独立非线性连接构造的里奇标量导出了仿射与度量方程，并在特定条件下恢复了经典结论。

A new construction of strict deformation quantization for Lagrangian fiber bundles

We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the quantum Hilbert spaces obtained by geometric quantization. The construction can be regarded as a "lattice approximation of the correspondence between differential operators and principal symbols". We analyze the corresponding formal deformation quantization. We also investigate into relations between our construction and Berezin-Toeplitz deformation quantization.