481 research outputs found
How large is the shadow of a symplectic ball?
Consider the image of a 2n-dimensional unit ball by an open symplectic
embedding into the standard symplectic vector space of dimension 2n. Its
2k-dimensional shadow is its orthogonal projection into a complex subspace of
real dimension 2k. Is it true that the volume of this 2k-dimensional shadow is
at least the volume of the unit 2k-dimensional ball? This statement is
trivially true when k = n, and when k = 1 it is a reformulation of Gromov's
non-squeezing theorem. Therefore, this question can be considered as a
middle-dimensional generalization of the non-squeezing theorem. We investigate
the validity of this statement in the linear, nonlinear and perturbative
setting.Comment: Final version, identical to the published one. Added comments about
the relationship with a conjecture of Viterbo and related references. Some of
the results of this paper are contained in our previous preprint
arXiv:1105.2931, which is no longer updated and will never become a published
articl
Rock flows
Rock flows are defined as forms of spontaneous mass movements, commonly found in mountainous countries, which have been studied very little. The article considers formations known as rock rivers, rock flows, boulder flows, boulder stria, gravel flows, rock seas, and rubble seas. It describes their genesis as seen from their morphological characteristics and presents a classification of these forms. This classification is based on the difference in the genesis of the rubbly matter and characterizes these forms of mass movement according to their source, drainage, and deposit areas
Symplectic Lefschetz fibrations on S^1 x M^3
In this paper we classify symplectic Lefschetz fibrations (with empty base
locus) on a four-manifold which is the product of a three-manifold with a
circle. This result provides further evidence in support of the following
conjecture regarding symplectic structures on such a four-manifold: if the
product of a three-manifold with a circle admits a symplectic structure, then
the three-manifold must fiber over a circle, and up to a self-diffeomorphism of
the four-manifold, the symplectic structure is deformation equivalent to the
canonical symplectic structure determined by the fibration of the
three-manifold over the circle.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper18.abs.htm
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