相关论文: Some new nonimmersion results for real projective …
In the series of our earlier papers on the subject, we proposed a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
In a recent work, F. Da Lio, M. Gianocca, and T. Rivi\`ere developped a new method to show upper semi-continuity results in geometric analysis, which they applied to conformally invariant Lagrangians in dimension $2$ (that include harmonic…
In this work we study differential geometry in $N$ dimensional Riemann curved spaces using Pfaff derivatives. Avoiding the classical partial derivative the Pfaff derivatives are constructed in a more sophisticated way and make evaluations…
We prove topological sphere theorems for RCD(n-1, n) spaces which generalize Colding's results and Petersen's result to the RCD setting. We also get an improved sphere theorem in the case of Einstein stratified spaces.
This paper extends parts of the results from [P.W.Michor and D. Mumford, \emph{Appl. Comput. Harmon. Anal.,} 23 (2007), pp. 74--113] for plane curves to the case of hypersurfaces in $\mathbb R^n$. Let $M$ be a compact connected oriented…
Ends and end cohomology are powerful invariants for the study of noncompact spaces. We present a self-contained exposition of the topological theory of ends and prove novel extensions including the existence of an exhaustion of a proper…
In this paper, we do the two things. 1. We present a formula to compute the rational cohomology ring of a real topological toric manifold, and thus that of a small cover or a real toric manifold, which implies the formula of Suciu and…
I am going to provide a new technique of approximating area under the curve, using the Newton-Raphson Method. I am also going to provide a formula that would help us approximate any Definite Integral or help us find the area under the…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
For an arrangement of $n$ lines in the real projective plane, we denote by $f$ the number of regions into which the real projective plane is divided by the lines. Using Bojanowski's inequality, we establish a new lower bound for $f$. In…
We use the mirror theorem for toric Deligne-Mumford stacks, proved recently by the authors and by Cheong-Ciocan-Fontanine-Kim, to compute genus-zero Gromov-Witten invariants of a number of toric orbifolds and gerbes. We prove a mirror…
In this work, we extend K. Kodaira's embedding theorem to non compact hermitian complex manifolds and laminations by complex manifolds.
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of…
We investigate projection constants within classes of multivariate polynomials over finite-dimensional real Hilbert spaces. Specifically, we consider the projection constant for spaces of spherical harmonics and spaces of homogeneous…
For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…
In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a probability measure to the space of discrete subgroups of…
We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half…
We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…