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Full-Text Articles in Physical Sciences and Mathematics
Linear Conditions Imposed On Flag Varieties, Julianna S. Tymoczko
Linear Conditions Imposed On Flag Varieties, Julianna S. Tymoczko
Mathematics Sciences: Faculty Publications
We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical analysis. We describe completely the homology of Hessenberg varieties over GLn(ℂ) and show that they have no odd-dimensional homology. We provide an explicit geometric construction which partitions each Hessenberg variety into pieces homeomorphic to affine space. We characterize these affine pieces by fillings of Young tableaux and show that the dimension of the affine piece can be computed by combinatorial rules generalizing the Eulerian numbers. We give an equivalent formulation of …
Conformality And Q-Harmonicity In Carnot Groups, Luca Capogna, Michael Cowling
Conformality And Q-Harmonicity In Carnot Groups, Luca Capogna, Michael Cowling
Mathematics Sciences: Faculty Publications
We show that if f is a 1-quasiconformal map defined on an open subset of a Carnot group G, then composition with f preserves Q-harmonic functions. We combine this with a regularity theorem for Q-harmonic functions and an algebraic regularity theorem for maps between Carnot groups to show that f is smooth. We give some applications to the study of rigidity.
Ahlfors Type Estimates For Perimeter Measures In Carnot-Carathéodory Spaces, Luca Capogna, Nicola Garofalo
Ahlfors Type Estimates For Perimeter Measures In Carnot-Carathéodory Spaces, Luca Capogna, Nicola Garofalo
Mathematics Sciences: Faculty Publications
We study the relationship between the geometry of hypersurfaces in a Carnot-Carathéodory (CC) space and the Ahlfors regularity of the corresponding perimeter measure. To this end we establish comparison theorems for perimeter estimates between an hypersurface and its tangent space, and between a CC geometry and its "tangent" Carnot group structure.
Local Energy Decay For Solutions Of Multi-Dimensional Isotropic Symmetric Hyperbolic Systems, Thomas C. Sideris, Becca Thomases
Local Energy Decay For Solutions Of Multi-Dimensional Isotropic Symmetric Hyperbolic Systems, Thomas C. Sideris, Becca Thomases
Mathematics Sciences: Faculty Publications
The local decay of energy is established for solutions to certain linear, multidimensional symmetric hyperbolic systems, with constraints. The key assumptions are isotropy and nondegeneracy of the associated symbols. Examples are given, including Maxwell's equations and linearized elasticity. Such estimates prove useful in treating nonlinear perturbations.
A Note On The Engulfing Property And The R 1+Α -Regularity Of Convex Functions In Carnot Groups, Luca Capogna, Diego Maldonado
A Note On The Engulfing Property And The R 1+Α -Regularity Of Convex Functions In Carnot Groups, Luca Capogna, Diego Maldonado
Mathematics Sciences: Faculty Publications
We study the engulfing property for convex functions in Carnot groups. As an application we show that the horizontal gradient of functions with this property is Hölder continuous.
Exponents For B-Stable Ideals, Eric Sommers, Julianna Tymoczko
Exponents For B-Stable Ideals, Eric Sommers, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
Let G be a simple algebraic group over the complex numbers containing a Borel subgroup B. Given a B-stable ideal I in the nilradical of the Lie algebra of B, we define natural numbers m 1, m 2,. . .,m k which we call ideal exponents. We then propose two conjectures where these exponents arise, proving these conjectures in types A n, B n, C n and some other types. When I = 0, we recover the usual exponents of G by Kostant (1959), and one of our conjectures reduces to a well-known factorization of the Poincaré polynomial of the …