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Characterizing the dual mixed volume via additive functionals  [PDF]
Paolo Dulio,Richard J. Gardner,Carla Peri
Mathematics , 2013,
Abstract: Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions) on a compact Hausdorff space. These are shown to yield characterizations of the dual mixed volume, the fundamental concept in the dual Brunn-Minkowski theory. The characterizations are shown to be best possible in the sense that none of the assumptions can be omitted. The results obtained are in the spirit of a similar characterization of the mixed volume in the classical Brunn-Minkowski theory, obtained recently by Milman and Schneider, but the methods employed are completely different.
Characterizing Volume Forms  [PDF]
Pierre Cartier,Marcus Berg,Cecile DeWitt-Morette,Alex Wurm
Physics , 2000,
Abstract: Old and new results for characterizing volume forms in functional integration.
From volume cone to metric cone in the nonsmooth setting  [PDF]
Nicola Gigli,Guido de Philippis
Mathematics , 2015,
Abstract: We prove that `volume cone implies metric cone' in the setting of RCD spaces, thus generalising to this class of spaces a well known result of Cheeger-Colding valid in Ricci-limit spaces.
The cone volume measure of antipodal points  [PDF]
Karoly J. B?r?czky,Pal Hegedus
Mathematics , 2014,
Abstract: The optimal condition of the cone volume measure of a pair of antopodal points is proved and analyzed.
Cone-volume measure and stability  [PDF]
Károly J. B?r?czky,Martin Henk
Mathematics , 2014,
Abstract: We show that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition. This implies, among others, a conjectured best possible inequality for the $\mathrm{U}$-functional of a convex body. For both results we provide stronger versions in the sense of stability inequalities.
Cone-volume measures of polytopes  [PDF]
Martin Henk,Eva Linke
Mathematics , 2013,
Abstract: The cone-volume measure of a polytope with centroid at the origin is proved to satisfy the subspace concentration condition. As a consequence a conjectured (a dozen years ago) fundamental sharp affine isoperimetric inequality for the U-functional is completely established -- along with its equality conditions.
Duality and Light Cone Symmetries of the Equations of Motion  [PDF]
Robert de Mello Koch,Jo?o P. Rodrigues
Physics , 1997, DOI: 10.1016/S0370-2693(98)00591-7
Abstract: The matrix theory description of the discrete light cone quantization of $M$ theory on a $T^{2}$ is studied. In terms of its super Yang- Mills description, we identify symmetries of the equations of motion corresponding to independent rescalings of one of the world sheet light cone coordinates, which show how the $S$ duality of Type IIB string theory is realized as a Nahm-type transformation. In the $M$ theory description this corresponds to a simple $9-11$ flip.
Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions  [PDF]
David F. Mross,Jason Alicea,Olexei I. Motrunich
Physics , 2015,
Abstract: We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in $(2+1)$ dimensions (QED$_3$) with $N = 1$ fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED$_3$ scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and $N = 2$ QED$_3$.
The movable cone via intersections  [PDF]
Brian Lehmann
Mathematics , 2011,
Abstract: We characterize the movable cone of divisors using intersections against curves on birational models.
The nef cone volume of generalized Del Pezzo surfaces  [PDF]
Ulrich Derenthal,Michael Joyce,Zach Teitler
Mathematics , 2007,
Abstract: We compute a naturally defined measure of the size of the nef cone of a Del Pezzo surface. The resulting number appears in a conjecture of Manin on the asymptotic behavior of the number of rational points of bounded height on the surface. The nef cone volume of a Del Pezzo surface Y with (-2)-curves defined over an algebraically closed field is equal to the nef cone volume of a smooth Del Pezzo surface of the same degree divided by the order of the Weyl group of a simply-laced root system associated to the configuration of (-2)-curves on Y. When Y is defined over a non-closed field of characteristic 0, a similar result holds, except that the associated root system is no longer necessarily simply-laced.
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