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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Presentations Of Rings With Non-Trivial Semidualizing Modules, David A. Jorgensen, Graham J. Leuschke, Sean Sather-Wagstaff
Presentations Of Rings With Non-Trivial Semidualizing Modules, David A. Jorgensen, Graham J. Leuschke, Sean Sather-Wagstaff
Mathematics - All Scholarship
Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and satisfies the condition HomR(C,C) \cong R. We prove that a Cohen-Macaulay ring R with dualizing module D admits a semidualizing module C satisfying R\ncong C \ncong D if and only if it is a homomorphic image of a Gorenstein ring in which the defining ideal decomposes in a cohomologically independent way. This expands on a well-known result of Foxby, Reiten and Sharp saying that R admits a dualizing module if and only if R is Cohen-Macaulay and a …
Non-Commutative Desingularization Of Determinantal Varieties, I, Ragnar-Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh
Non-Commutative Desingularization Of Determinantal Varieties, I, Ragnar-Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh
Mathematics - All Scholarship
We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.
Area Contraction For Harmonic Automorphisms Of The Disk, Ngin-Tee Koh, Leonid V. Kovalev
Area Contraction For Harmonic Automorphisms Of The Disk, Ngin-Tee Koh, Leonid V. Kovalev
Mathematics - All Scholarship
A harmonic self-homeomorphism of a disk does not increase the area of any concentric disk.
The Nitsche Conjecture, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
The Nitsche Conjecture, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
The conjecture in question concerns the existence of a harmonic homeomorphism between circular annuli A(r,R) and A(r*,R*), and is motivated in part by the existence problem for doubly-connected minimal surfaces with prescribed boundary. In 1962 J.C.C. Nitsche observed that the image annulus cannot be too thin, but it can be arbitrarily thick (even a punctured disk). Then he conjectured that for such a mapping to exist we must have the following inequality, now known as the Nitsche bound: R*/r* is greater than or equal to (R/r+r/R)/2. In this paper we give an affirmative answer to his conjecture. As a corollary, …
Additive Maps Preserving The Reduced Minimum Modulus Of Banach Space Operators, Abdellatif Bourhim
Additive Maps Preserving The Reduced Minimum Modulus Of Banach Space Operators, Abdellatif Bourhim
Mathematics - All Scholarship
Let B(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We prove that an additive surjective map phi on B(X) preserves the reduced minimum modulus if and only if either there are bijective isometries U:X -> X and V:X -> X both linear or both conjugate linear such that phi(T)=UTV for all T in B(X), or X is reflexive and there are bijective isometries U:X* -> X and V:X -> X* both linear or both conjugate linear such that phi(T)=UT*V for all T in B(X). As immediate consequences …
Contact Process In A Wedge, J. Theodore Cox, Nevena Maric, Rinaldo Schinazi
Contact Process In A Wedge, J. Theodore Cox, Nevena Maric, Rinaldo Schinazi
Mathematics - All Scholarship
We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an application we show that a type of weak coexistence is possible in the nearest-neighbor "grass-bushes-trees'' successional model introduced in Durrett and Swindle (1991).
A Remark On The Topology Of (N,N) Springer Varieties, Stephan M. Wehrli
A Remark On The Topology Of (N,N) Springer Varieties, Stephan M. Wehrli
Mathematics - All Scholarship
We prove a conjecture of Khovanov [Kho04] which identifies the topological space underlying the Springer variety of complete flags in C2n stabilized by a fixed nilpotent operator with two Jordan blocks of size n.
Khovanov Homology, Sutured Floer Homology, And Annular Links, J. Elisenda Grigsby, Stephan M. Wehrli
Khovanov Homology, Sutured Floer Homology, And Annular Links, J. Elisenda Grigsby, Stephan M. Wehrli
Mathematics - All Scholarship
Lawrence Roberts, extending the work of Ozsvath-Szabo, showed how to associate to a link, L, in the complement of a fixed unknot, B in S3, a spectral sequence from the Khovanov homology of a link in a thickened annulus to the knot Floer homology of the preimage of B inside the double-branched cover of L. In a previous paper, we extended Ozsvath-Szabo's spectral sequence in a different direction, constructing for each knot K in S3 and each positive integer n, a spectral sequence from Khovanov's categorification of the reduced, n-colored Jones polynomial to the sutured Floer homology …
On The Naturality Of The Spectral Sequence From Khovanov Homology To Heegaard Floer Homology, J. Elisenda Grigsby, Stephan M. Wehrli
On The Naturality Of The Spectral Sequence From Khovanov Homology To Heegaard Floer Homology, J. Elisenda Grigsby, Stephan M. Wehrli
Mathematics - All Scholarship
Ozsvath and Szabo have established an algebraic relationship, in the form of a spectral sequence, between the reduced Khovanov homology of (the mirror of) a link L in S3 and the Heegaard Floer homology of its double-branched cover. This relationship has since been recast by the authors as a specific instance of a broader connection between Khovanov- and Heegaard Floer-type homology theories, using a version of Heegaard Floer homology for sutured manifolds developed by Juhasz. In the present work we prove the naturality of the spectral sequence under certain elementary TQFT operations, using a generalization of Juhasz's surface decomposition …
Quasiplurisubharmonic Green Functions, Dan Coman, Vincent Guedj
Quasiplurisubharmonic Green Functions, Dan Coman, Vincent Guedj
Mathematics - All Scholarship
Given a compact Kahler manifold X, a quasiplurisubharmonic function is called a Green function with pole at p in X if its Monge-Ampere measure is supported at p. We study in this paper the existence and properties of such functions, in connection to their singularity at p. A full characterization is obtainedin concrete cases, such as (multi)projective spaces.
An N-Dimensional Version Of The Beurling-Ahlfors Extension, Leonid V. Kovalev, Jani Onninen
An N-Dimensional Version Of The Beurling-Ahlfors Extension, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
We extend monotone quasiconformal mappings from dimension n to n+1 while preserving both monotonicity and quasiconformality. The extension is given explicitly by an integral operator. In the case n=1 it yields a refinement of the Beurling-Ahlfors extension.
Mutation Invariance Of Khovanov Homology Over F_2, Stephan M. Wehrli
Mutation Invariance Of Khovanov Homology Over F_2, Stephan M. Wehrli
Mathematics - All Scholarship
We prove that Khovanov homology and Lee homology with coefficients in F2=Z/2Zare invariant under component-preserving link mutations.
Harmonic Mappings Of An Annulus, Nitsche Conjecture And Its Generalizations, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Harmonic Mappings Of An Annulus, Nitsche Conjecture And Its Generalizations, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
As long ago as 1962 Nitsche conjectured that a harmonic homeomorphism h: A(r,R) onto-> A(r*, R*) between planar annuli exists if and only if R*/r* > 1/2 ((R/r) + (r/R)). We prove this conjecture when the domain annulus is not too wide; explicitly, when log(R/r) < 3/2. For general A(r,R) the conjecture is proved under additional assumption that either h or its normal derivative have vanishing average on the inner boundary circle. This is the case for the critical Nitsche mapping which yields equality in the above inequality. The Nitsche mapping represents so-called free evolution of circles of the annulus A(r,R). It will be shown on the other hand that forced harmonic evolution results in greater ratio R*/r*. To this end, we introduce the underlying differential operators for the circular means of the forced evolution and use them to obtain sharp lower bounds of R*/r*.