Searcharxiv⌕ Search

arXiv · 2609.37794

The Ekeland--Hofer--Zehnder Capacity of rotated $L_p$-Ellipsoid

Abstract

We find explicit formulas for the EHZ and cylindrical capacities of rotated $L_{p}$-ellipsoids. In addition, we provide an algorithm to estimate the EHZ capacity.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vardan Oganesyan. 2026-09-29. The Ekeland--Hofer--Zehnder Capacity of rotated $L_p$-Ellipsoid. https://arxiv.org/abs/2609.37794

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Poisson $C^\infty$-schemes

We introduce Poisson $C^\infty$-rings and Poisson local $C^\infty$-ringed spaces. We show that the spectrum of a Poisson $C^\infty$-ring is an affine Poisson $C^\infty$-scheme. We then discuss applications that include singular symplectic and Poisson reductions, singular quasi-Poisson reduction, coisotropic reduction and Poisson-Dirac subschemes.

math.SG↗

The derived Picard group of Fukaya categories of closed surfaces

Let $Σ_g$ be a closed oriented surface of genus $g\geq2$, and let $\mathscr F_g$ be its split-closed, strictly unobstructed, two-periodic Fukaya category over the complex Novikov field $Λ$. We determine the derived Picard group \[ \operatorname{DPic}_Λ(\mathscr F_g) \cong \bigl(H^1(Σ_g;Λ^\times) \rtimesπ_0\operatorname{Diff}^+(Σ_g)\bigr) \times\mathbb Z/2\mathbb Z. \] This proves the enhanced form of the conjecture of arXiv:2006.09689. As a corollary, we obtain that the derived Picard group itself determines the genus of the surface.

math.SG↗

Weighted Seshadri constants and ellipsoid embeddings

We explore Seshadri constants associated to weighted blow-ups of complex projective varieties and demonstrate how to use this notion to construct symplectic embeddings of ellipsoids. We illustrate the utility of this point of view by providing constructions of full fillings of $\mathbb{CP}^2$ by ellipsoids corresponding to all of the exceptional (post-Fibonacci) steps of the McDuff--Schlenk staircase and some non-obvious embeddings of ellipsoids in ellipsoids.

math.SG↗