Related papers: Arc lifting for the Nash manifold

The Nash blowing-up (or modification) of an algebraic variety $X$ is a canonical process that produces a proper, birational morphism $\pi : X' \to X$ of varieties. It is expected that the singularities of $X'$ will be better than those of…

This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.

Criteria for a diffeomorphism of a smooth manifold $M$ to be lifted to a linear automorphism of a given real vector bundle $p\colon V\rightarrow M$, are stated. Examples are included and the metric and complex vector-bundle cases are also…

Let $S$ be a compact Hausdorff space and $X$ a complex manifold. We consider the space $C(S,X)$ of continuous maps $S\to X$, and prove that any bounded holomorphic function on this space can be continued to a holomorphic function, possibly…

In this paper, we establish new Laplacian comparison theorems and rigidity theorems for complete K\"ahler manifolds under new curvature notions that interpolate between Ricci curvature and holomorphic bisectional curvature.

We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.

We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann--Roch theorem.

We present a simple geometric construction for smoothing polyhedral utility functions. Keywords: Afriat- Varian theorem, the utility function, the economic indices theory, convex analysis.

Let $N$ be a closed spin manifold with positive scalar curvature and $D_N$ the Dirac operator on $N$. Let $M_1$ and $M_2$ be two Galois covers of $N$ such that $M_2$ is a quotient of $M_1$. Then the quotient map from $M_1$ to $M_2$…

In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.

The purpose of this note is to give a direct and self-contained proof of the Proportionality Theorem of Brasselet-Schwartz. This theorem relates the Schwartz indices of frames obtained by radial extension on Whitney stratified analytic…

In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone. Such a representation or 'lift' of the convex set is especially useful if the…

Updated version of 2013 Arizona WInter School notes on modularity lifting theorems for for two-dimensional p-adic representations, using wherever possible arguments that go over to the n-dimensional (self-dual) case.

In this paper, we introduce a new subclass of close-to-convex harmonic functions. We present a sufficient coefficient condition for a function to be a member of this class. Furthermore, we establish a distortion theorem. These results lay…

The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.

We pose a normal form of transition functions along some Levi-flat hypersurfaces obtained by suspension. By focusing on methods in circle dynamics and linearization theorems, we give a sufficient condition to obtain a normal form as a…

The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forelli's theorem on the complex analyticity of the functions that are: (1) $\mathcal{C}^\infty$…

Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction…

In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.

One important class of tools in the study of the connections between algebraic and topological structures are the "Banach-Stone type theorems", which describe algebraic isomorphisms of algebras (or groups, lattices, etc.) of functions in…