The Symplectic Size of a Randomly Rotated Convex Body
In this note we study the expected value of certain symplectic capacities of randomly rotated centrally symmetric convex bodies in the classical phase space.
math.SG↗
arXiv subjects
Efim D. Gluskin
Publications and source records attributed to Efim D. Gluskin.
A remark on projections of the rotated cube to complex lines
Motivated by relations with a symplectic invariant known as the "cylindrical symplectic capacity", in this note we study the expectation of the area of a minimal projection to a complex line for a randomly rotated cube.
math.MG↗
Asymptotic Equivalence of Symplectic Capacities
A long-standing conjecture states that all normalized symplectic capacities coincide on the class of convex subsets of ${\mathbb R}^{2n}$. In this note we focus on an asymptotic (in the dimension) version of this conjecture, and show that when restricted to the class of centrally symmetric convex bodies in ${\mathbb R}^{2n}$, several symplectic capacities, including the Ekeland-Hofer-Zehnder capacity, the displacement energy capacity, and the cylindrical capacity, are all equivalent up to an absolute constant.
math.SG↗