相关论文: Acyclic embeddings of open Riemann surfaces into n…

We study the orchard problem on cubic surfaces. We classify possibly reducible cubic surfaces $X\subseteq \mathbb{P}^3(\C)$ with smooth components on which there exist families of finite sets (of unbounded size) with quadratically many…

We prove here that given a proper isometric action $K\times M\to M$ on a complete Riemannian manifold $M$ then every continuous isometric flow on the orbit space $M/K$ is smooth, i.e., it is the projection of an $K$-equivariant smooth flow…

We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group $G$…

We investigate a large class of elliptic differential inclusions on non-compact complete Riemannian manifolds which involves the Laplace-Beltrami operator and a Hardy-type singular term. Depending on the behavior of the nonlinear term and…

We propose a general theory of the Open Gromov-Witten invariant on Calabi-Yau three-folds. We introduce the moduli space of multi-curves and show how it leads to invariants. Our construction is based on an idea of Witten. In the special…

An oriented closed connected N-manifold M is inflexible if it does not admit self-maps of unbounded degree. In addition, if all the maps from any other oriented closed connected N-manifold have bounded degree, then M is said to be strongly…

This note is about the interplay between the almost-hermitian and Riemannian geometries of a manifold. These geometries can be seen to interact through curvature. The main result is an obstruction equation to the integrability of…

In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the…

We prove two rigidity theorems for maps between Riemannian manifolds. First, we prove that a Lipschitz map $f:M\to N$ between two oriented Riemannian manifolds, whose differential is almost everywhere an orientation-preserving isometry, is…

The elliptic-matrix quantum Olshanetsky-Perelomov problem is introduced for arbitrary root systems by means of an elliptic generalization of the Dunkl operators. Its equivalence with the double affine generalization of the…

We provide two new proofs of a theorem of Cooper, Long and Reid which asserts that, apart from an explicit finite list of exceptional manifolds, any compact orientable irreducible 3-manifold with non-empty boundary has large fundamental…

Let (M,w,L) be a symplectic manifold endowed with a lagrangian foliation L. Liberman and Weinstein have shown that the leaves of L are endowed with an affine structure. In this paper we provide links between the theories of affine manifolds…

The Geometric Shafarevich Conjecture and the Theorem of de Franchis state the finiteness of the number of certain holomorphic objects on closed or punctured Riemann surfaces. The analog of these kind of theorems for Riemann surfaces of…

We show the smoothness of weakly Dirac-harmonic maps from a closed spin Riemann surface into stationary Lorentzian manifolds, and obtain a regularity theorem for a class of critical elliptic systems without anti-symmetry structures.

We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…

Following the work of Castano-Bernard and Matessi on conifold transition in the Gross-Siebert program, we construct orbi-conifold transitions of the Shoen's Calabi-Yau threefold and their mirrors. The construction glues together the local…

We give a proof of the following theorem of M. Gromov (Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc., 2 (1989), 851-897). Let Z be a holomorphic fiber bundle over a Stein manifold. If the fiber of Z…

The paper is related to the author's talk at the Hayama Symposium in Complex Analysis in December 2000. In section 1 we survey results on the Oka principle for sections of holomorphic submersions over Stein manifolds. In section 2 we apply…

We study the existence of proper holomorphic embeddings of bordered Riemann surfaces into the complex plane C^2. Denote by M(R) the moduli space consisting of all equivalence classes of complex structures J on a given smooth oriented…

In his 1970 ICM report, Sullivan proposes the program of l-adic formalization of the concept of manifolds. In this program, he claims that smooth positive characteristic varieties should carry l-adic formal manifold structures. He also…