相关论文: Remarks on weakly pseudoconvex boundaries

On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. Moreover, this result may be localized to compact subdomains in…

We construct a canonical pseudofunctor ^# on the category of finite-type maps of (say) connected noetherian universally catenary finite-dimensional separated schemes, taking values in the category of Cousin complexes. This pseudofunctor is…

We study weak solutions to degenerate quasilinear elliptic equations, involving first order terms, in unbounded tubular domains. In particular we show that, under suitable hypotheses, the weak comparison principle holds if the domain is…

The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of…

We introduce the concept of partial Poisson structure on a manifold $M$ modelled on a convenient space. This is done by specifying a (weak) subbundle $T^{\prime}M$ of $T^{\ast}M$ and an antisymmetric morphism $P:T^{\prime}M\rightarrow TM$…

In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds related to modules at boundary…

This work consists of two parts. In the first part, we consider a compact connected strongly pseudoconvex CR manifold $X$ with a transversal CR $S^{1}$ action. We establish an equidistribution theorem on zeros of CR functions. The main…

We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.

Given an $S^1$-manifold with isolated fixed points, some recent papers are concerned with the relationship between the least number of fixed points and the characteristic numbers of this manifold, and their proofs have some similar…

We show that for any bounded domain $\Omega\subset\Cp ^n$ of 1-type $2k $ which is locally convexifiable at $p\in b\Omega$, having a Stein neighborhood basis, there is a biholomorphic map $f:\bar{\Omega}\rightarrow \Cp ^n $ such that $f(p)$…

We point out an effect which may stabilize a supersymmetric membrane moving on a manifold with boundary, and lead to a light-cone Hamiltonian with a discrete spectrum of eigenvalues. The analysis is carried out explicitly for a closed…

We study the pseudohermitian sectional curvature of a CR manifold.

For a class of discrete quasi convex functions called semi-strictly quasi M$^\natural$-convex functions, we investigate fundamental issues relating to minimization, such as optimality condition by local optimality, minimizer cut property,…

We give a potential theoretic characterization for compactness of the dbar-Neumann problem on smooth bounded pseudoconvex domains in C^n.

Let M be a compact, orientable, mean convex 3-manifold with boundary. We show that the set of all simple closed curves in the boundary of M which bound unique area minimizing disks in M is dense in the space of simple closed curves in the…

We study geometric properties of compact stable minimal surfaces with boundary in homogeneous 3-manifolds $X$ that can be expressed as a semidirect product of $\mathbb{R}^2$ with $\mathbb{R}$ endowed with a left invariant metric. For any…

We study the large-scale geometry of 3-manifolds with nontrivial 2-dimensional bounded cohomology, with a view to proving a weak version of the geometrization conjecture for such manifolds.

In this paper, we define weakly coherent rings, and examine the transfer of these rings to homomorphic image, trivial ring extension, localization, and direct product. These results provide examples of weakly coherent rings that are not…

It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…

In the paper we consider boundary -- value problems with rapidly alternating type of boundary conditions, including problems in domains with perforated boundaries. We present the classification of homogenized (limit) problems depending on…