相关论文: Algebraic dependence and finiteness problems of di…

We enumerate a necessary condition for the existence of infinitely many geometrically distinct, non-constant, prime closed geodesics on an arbitrary closed Riemannian manifold $M$. That is, we show that any Riemannian metric on $M$ admits…

In this paper, we investigate meromorphic solutions in $\mathbb{C}^m$ of the nonlinear differential equation \[\displaystyle f^n\partial_u(f)g^n\partial_u(g)=1,\] where $\partial_u(f)=\sum_{j=1}^mu_j\partial_j(f)$ and $\sum_{j=1}^m u_j\neq…

We prove that the characteristic foliation $F$ on a non-singular divisor $D$ in an irreducible projective hyperkaehler manifold $X$ cannot be algebraic, unless the leaves of $F$ are rational curves or $X$ is a surface. More generally, we…

The purpose of this article is to show that the bivariant algebraic $A$-cobordism groups considered previously by the author are independent of the chosen base ring $A$. This result is proven by analyzing the bivariant ideal generated by…

We study the period map from infinitesimal deformations of a scheme $X$ over a perfect field $k$ to those of the associated $k$-linear $\infty$-category $\mathrm{QC}(X)$. For quasicompact, smooth, and separated $X$, we identify the…

On a 6-dimensional, conformal, oriented, compact manifold $M$ without boundary, we compute a whole family of differential forms $\Omega_6(f,h)$ of order 6, with $f,h \in C^\infty(M).$ Each of these forms will be symmetric on $f,$ and $h,$…

We use the method of equivariant moving frames to revisit the problem of normal forms and equivalence of nondegenerate real hypersurfaces M \subset C^2 under the pseudo-group action of holomorphic transformations. The moving frame…

This paper deals with random perturbations of diffeomorphisms on n-dimensional Riemannian manifolds with distributions supported on k-dimensional disks, where k<n. First we demonstrate general but not very intuitive conditions which…

We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictions $\mathcal M_V$ of the multiplier algebra $\mathcal M$ of Drury-Arveson space to a holomorphic subvariety…

The $h$-version of the finite-element method ($h$-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now rigorously understood that (using piecewise polynomials of…

In this paper, we will show that if two meromorphic mappings $f$ and $g$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ have the same inverse images for $(2n+2)$ moving hyperplanes $\{a_i\}_{i=1}^{2n+2}$ with multiplicities counted to level…

In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex…

We give four constructions of non-$\partial\bar\partial$ (hence non-K\"ahler) manifolds: (1) A simply connected page-$1$-$\partial\bar\partial$-manifold (2) A simply connected $dd^c+3$-manifold (3) For any $r\geq 2$, a simply connected…

We prove the following finite jet determination result for CR mappings: Given a smooth generic submanifold M of C^N, N >= 2, which is essentially finite and of finite type at each of its points, for every point p on M there exists an…

We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of C^n fixing the origin such that df_O is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to C^n, a…

In this article, we construct explicit meromorphic solutions of first order linear $q$-difference equations in the complex domain and we describe the location of all their zeros and poles. The homogeneous case leans on the study of four…

In this paper, we study the uniqueness of the differential-difference of meromorphic functions. We prove the following result: Let $f$ be a nonconstant meromorphic function of $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number,…

We investigate the manifold $\cal{M}$ of (real) quadratic forms in n > 1 variables having a multiple eigenvalue. In addition to known facts, we prove that 1) $\cal{M}$ is irreducible, 2) in the case of n = 3, scalar matrices and only them…

We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal…

We study the (in)dependence of additivity and homogeneity conditions in the definition of linear mappings between vector spaces over the same scalar field. Unlike other works on the subject, dealing with particular fields like real or…