相关论文: On Z-compactifiability of manifolds

In this article, we prove a sharp estimate for the solutions to parabolic equations on manifolds. Precisely, using symmetrization techniques and isoperimetric inequalities on Riemannian manifold, we obtain a Bandle's comparison on complete…

In this article, we show the existence of conjugations on many simply-connected spin 6-manifolds with free integral cohomology. In a certain class the only condition on X^6 to admit a conjugation with fixed point set M^3 is the obvious one:…

Developing A.D. Aleksandrov's ideas, the first-named author of this article proposed the following approach to study of rigidity problems for the boundary of a $C^0$-submanifold in a smooth Riemannian manifold: Let $Y_1$ be a 2-dimensional…

We study the existence of topologically closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any noncompact complex space admitting an exhaustion function whose Levi…

We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other…

Let $G$ be a connected unimodular group equipped with a (left and hence right) Haar measure $\mu_G$, and suppose $A, B \subseteq G$ are nonempty and compact. An inequality by Kemperman gives us…

We study the rigidity of compact submanifolds of Riemannian manifolds of arbitrary codimension that satisfy a sharp pinching condition involving the norm of the second fundamental form and the mean curvature. Without assuming that the…

Let (M,g) be a four or six dimensional compact Riemannian manifold which is locally conformally flat and assume that its boundary is totally umbilical. In this note, we prove that if the Euler characteristic of M is equal to 1 and if its…

A compact real analytic Riemannian manifold M admits a canonical complexification with plurisubharmonic exhaustion function satisfying the homogeneous complex Monge-Ampere equation, called a Grauert tube. From the point of view of complex…

We show that a necessary and sufficient condition for a smooth function on the tangent bundle of a manifold to be a Lagrangian density whose action can be minimized is, roughly speaking, that it be the sum of a constant, a nonnegative…

Let a real-analytic manifold $M$ formally (holomorphically) equivalent to the following model…

The Hirzebruch signature formula provides an obstruction to the following realization question: given a rational Poincar\'e duality algebra $\mathcal{A}$, does there exist a smooth manifold $M$ such that $H^*(M;\mathbb{Q})=\mathcal{A}$?…

Consider a Hamiltonian circle action on a closed $8$-dimensional symplectic manifold $M$ with exactly five fixed points, which is the smallest possible fixed set. In their paper, L. Godinho and S. Sabatini show that if $M$ satisfies an…

We establish necessary and sufficient conditions for the closedness of the range of a class of first-order differential operators associated with an involutive structure on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold…

We derive a necessary condition for compactness of the weighted $\overline\partial$-Neumann operator on the space $L^2(\mathbb C^n,e^{-\varphi})$, under the assumption that the corresponding weighted Bergman space of entire functions has…

We prove that if a compact, simply connected Riemannian $G$-manifold $M$ has orbit space $M/G$ isometric to some other quotient $N/H$ with $N$ having zero topological entropy, then $M$ is rationally elliptic. This result, which generalizes…

Let $M$ be a compact manifold with an effective semi-free circle action whose fixed point set has trivial normal bundle. We prove that its cotangent bundle endowed with the canonical symplectic form has bounded Hofer-Zehnder sensitive…

We introduce the concept of Hofer-Zehnder $G$-semicapacity (or $G$-sensitive Hofer-Zehnder capacity) and prove that given a geometrically bounded symplectic manifold $(M,\omega)$ and an open subset $N \subset M$ endowed with a Hamiltonian…

In this paper, we establish Chern number identities on compact complex surfaces. As an application, we prove that if $(M,g)$ is a compact Riemannian four-manifold with constant scalar curvature and admits a compatible complex structure $J$…

We prove a compactness theorem for embedded measured hyperbolic Riemann surface laminations in a compact almost complex manifold $(X, J)$. To prove compactness result, we show that there is a suitable topology on the space of measured…