The Experts below are selected from a list of 31794 Experts worldwide ranked by ideXlab platform

Denis S. Krotov - One of the best experts on this subject based on the ideXlab platform.

Frank Loray - One of the best experts on this subject based on the ideXlab platform.

  • Singular foliations with trivial canonical class
    Inventiones mathematicae, 2018
    Co-Authors: Frank Loray, Jorge Vitório Pereira, Frédéric Touzet
    Abstract:

    This paper describes the structure of singular Codimension one foliations with numerically trivial canonical bundle on complex projective manifolds.

  • a preparation theorem for Codimension one foliations
    Annals of Mathematics, 2006
    Co-Authors: Frank Loray
    Abstract:

    After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of Codimension-one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of Levinson-Moser for functions, Dufour-Zhitomirskii for nondegenerate Codimension-one foliations (proving in turn the analyticity), Str?oyzyna- y Zoladek for non degenerate planar vector fields and Bruno-?Ecalle for saddle-node foliations in the plane.

  • a preparation theorem for Codimension one foliations
    arXiv: Differential Geometry, 2004
    Co-Authors: Frank Loray
    Abstract:

    After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of Codimension one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of Levinson-Moser for functions, Dufour-Zhitomirskii for non degenerate Codimension 1 foliations (proving in turn the analyticity), Strozyna-Zoladek for non degenerate planar vector fields and Brjuno-Ecalle for saddle-node foliations in the plane.

Fernanda Pambianco - One of the best experts on this subject based on the ideXlab platform.

  • New covering codes of radius R, Codimension tR and $$tR+\frac{R}{2}$$ t R +
    Designs Codes and Cryptography, 2019
    Co-Authors: Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco
    Abstract:

    The length function $$\ell _q(r,R)$$ ℓ q ( r , R ) is the smallest length of a q -ary linear code of Codimension r and covering radius R . In this work we obtain new constructive upper bounds on $$\ell _q(r,R)$$ ℓ q ( r , R ) for all $$R\ge 4$$ R ≥ 4 , $$r=tR$$ r = t R , $$t\ge 2$$ t ≥ 2 , and also for all even $$R\ge 2$$ R ≥ 2 , $$r=tR+\frac{R}{2}$$ r = t R + R 2 , $$t\ge 1$$ t ≥ 1 . The new bounds are provided by infinite families of new covering codes with fixed R and increasing Codimension. The new bounds improve upon the known ones. We propose a general regular construction (called “Line+Ovals”) of a minimal $$\rho $$ ρ -saturating $$((\rho +1)q+1)$$ ( ( ρ + 1 ) q + 1 ) -set in the projective space $$\mathrm {PG}(2\rho +1,q)$$ PG ( 2 ρ + 1 , q ) for all $$\rho \ge 0$$ ρ ≥ 0 . Such a set corresponds to an $$[Rq+1,Rq+1-2R,3]_qR$$ [ R q + 1 , R q + 1 - 2 R , 3 ] q R locally optimal code of covering radius $$R=\rho +1$$ R = ρ + 1 . Basing on combinatorial properties of these codes regarding to spherical capsules, we give constructions for code Codimension lifting and obtain infinite families of new surface-covering codes with Codimension $$r=tR$$ r = t R , $$t\ge 2$$ t ≥ 2 . In addition, we obtain new 1-saturating sets in the projective plane $$\mathrm {PG}(2,q^2)$$ PG ( 2 , q 2 ) and, basing on them, construct infinite code families with fixed even radius $$R\ge 2$$ R ≥ 2 and Codimension $$r=tR+\frac{R}{2}$$ r = t R + R 2 , $$t\ge 1$$ t ≥ 1 .

  • Linear codes with covering radius 2, 3 and saturating sets in projective geometry
    IEEE Transactions on Information Theory, 2004
    Co-Authors: A.a. Davydov, Stefano Marcugini, Fernanda Pambianco
    Abstract:

    Infinite families of linear codes with covering radius R=2, 3 and Codimension tR+1 are constructed on the base of starting codes with Codimension 3 and 4. Parity-check matrices of the starting codes are treated as saturating sets in projective geometry that are obtained by computer search using projective properties of objects. Upper bounds on the length function and on the smallest sizes of saturating sets are given.

Abdol-reza Mansouri - One of the best experts on this subject based on the ideXlab platform.

  • Topological Obstructions to Submanifold Stabilization
    IEEE Transactions on Automatic Control, 2010
    Co-Authors: Abdol-reza Mansouri
    Abstract:

    We consider the problem of local asymptotic feedback stabilization-via a continuously differentiable feedback law-of a control system ẋ = f(x,u) defined in Euclidean space Rn (with f being continuously differentiable) to a compact, connected, oriented m-dimensional submanifold M of Rn with Codimension strictly larger than one. We obtain necessary conditions on the topology of M for such a stabilizing feedback law to exist. This extends the work done in, where only the Codimension one case was treated. We also briefly discuss the case where the control is only assumed continuous.

William P. Minicozzi - One of the best experts on this subject based on the ideXlab platform.

  • Complexity of parabolic systems
    Publications mathématiques de l'IHÉS, 2020
    Co-Authors: Tobias Holck Colding, William P. Minicozzi
    Abstract:

    We first bound the Codimension of an ancient mean curvature flow by the entropy. As a consequence, all blowups lie in a Euclidean subspace whose dimension is bounded by the entropy and dimension of the evolving submanifolds. This drastically reduces the complexity of the system. We use this in a major application of our new methods to give the first general bounds on generic singularities of surfaces in arbitrary Codimension. We also show sharp bounds for Codimension in arguably some of the most important situations of general ancient flows. Namely, we prove that in any dimension and Codimension any ancient flow that is cylindrical at − ∞ $-\infty $ must be a flow of hypersurfaces in a Euclidean subspace. This extends well-known classification results to higher Codimension. The bound on the Codimension in terms of the entropy is a special case of sharp bounds for spectral counting functions for shrinkers and, more generally, ancient flows. Shrinkers are solutions that evolve by scaling and are the singularity models for the flow. We show rigidity of cylinders as shrinkers in all dimension and all Codimension in a very strong sense: Any shrinker, even in a large dimensional space, that is sufficiently close to a cylinder on a large enough, but compact, set is itself a cylinder. This is an important tool in the theory and is key for regularity; cf. (Colding and Minicozzi II in preprint, 2020 ).

  • Entropy and Codimension bounds for generic singularities
    arXiv: Differential Geometry, 2019
    Co-Authors: Tobias H. Colding, William P. Minicozzi
    Abstract:

    We show that all closed $2$-dimensional singularities for higher Codimension mean curvature flow that cannot be perturbed away have uniform entropy bounds and lie in a linear subspace of small dimension. The entropy and dimension of the subspace are both $\leq C\,(1+\gamma)$ for some universal constant $C$ and genus $\gamma$. These are the first general bounds on generic singularities in arbitrary Codimension.