Related papers: Cube normalized symplectic capacities
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.
It is a long-standing conjecture that all symplectic capacities which are equal to the Gromov width for ellipsoids coincide on a class of convex domains in $\mathbb{R}^{2n}$. It is known that they coincide for monotone toric domains in all…
We define a capacity which measures the size of Weinstein tubular neighbourhoods of Lagrangian submanifolds. In symplectic vector spaces this leads to bounds on the codisc radius for any closed Lagrangian submanifold in terms of Viterbo's…
It is well known that derivatives of solutions to elliptic boundary value problems may become unbounded near the corner of a domain with a conical singularity, even if the data are smooth. When the corner domain is approximated by more…
In this note we apply the billiard technique to deduce some results on Viterbo's conjectured inequality between volume of a convex body and its symplectic capacity. We show that the product of a permutohedron and a simplex (properly related…
We describe the semigroup of the Lipschitz saturation of a complex analytic toric singularity in arbitrary dimension. We give a necessary and sufficient condition for a monomial in the normalization to belong to the Lipschitz saturation, in…
In this short note, we construct an explicit embedding of the rescaling of the $p$-sum $K\oplus_p K^{\circ}$ of the centrally symmetric convex domain $K$ and its polar $K^{\circ}$ to the product $K \times K^{\circ}$. The rescaling constant…
In this paper our aim is to present some monotonicity and convexity properties for the one dimensional regularization of the Coulomb potential, which has applications in the study of atoms in magnetic fields and which is in fact a…
We provide a lower bound for the embedding capacity of higher-dimensional symplectic ellipsoids, formulated in terms of the Lagrangian capacity of ellipsoids. Our approach relies on examining the Borman--Sheridan class of a Weinstein…
In this note we consider two topics involving the relationship between the symplectic capacity and the mean width of convex bodies in $\mathbb{R}^{2n}$. We first describe an alternative path from the symplectic Brunn-Minkowski inequality of…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
For a convex domain in the standard Euclidean symplectic space which is invariant under a linear anti-symplectic involution $\tau$ we show that its Ekeland-Hofer-Zehnder capacity is equal to the $\tau$-symmetrical symplectic capacity of it.
We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the $p$-Laplace operator and a general nonlinearity satisfying concavity type assumptions. This provides an…
In this paper we settle three basic questions concerning the Gutt-Hutchings capacities. Our primary result settles a version of the recognition question in the negative. We prove that the Gutt-Hutchings capacities together with the volume,…
In this paper we give concrete estimations for the pseudo symplectic capacities of toric manifolds in combinatorial data. Some examples are given to show that our estimates can compute their pseudo symplectic capacities. As applications we…
Motivated by work of the first author, this paper studies symplectic embedding problems of lagrangian products that are sufficiently symmetric. In general, lagrangian products arise naturally in the study of billiards. The main result of…
We extend the notion of polar duality to pairs of transverse Lagrangian planes in the standard symplectic space. This allows us to show that polar duality has a natural interpretation in terms of symplectic geometry. We apply our results to…
We show that on the unit disc cotangent bundle of flat Riemannian tori, all normalized capacities coincide with twice the systole. The same result holds for flat, reversible Finsler tori and normalized capacities that are greater than or…
We prove an analogue of the 4-dimensional local Viterbo conjecture for the higher Ekeland-Hofer capacities: on the space of 4-dimensional smooth star-shaped domains of unitary volume, endowed with the $C^3$ topology, the local maximizers of…
We derive a general formula for the RG improved effective (Coleman-Weinberg) potential for classically conformal models, applying it to several examples of physical interest, and in particular a model of QCD coupled via quarks to a…