Extremal Length in Higher Dimensions and Complex Systolic Inequalities

Pacini, Tommaso

doi:10.1007/s12220-020-00467-2

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…After the first version of the present article was posted online, Haiden [13] proves a systolic inequality for certain higher-dimensional symplectic torus, and Pacini [25] proposes a higherdimensional generalization of extremal lengths and complex systolic inequalities.…”

Section: Related Workmentioning

confidence: 98%

Systolic inequalities for K3 surfaces via stability conditions

Fan

2021

Math. Z.

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We introduce the notions of categorical systoles and categorical volumes of Bridgeland stability conditions on triangulated categories. We prove that for any projective K3 surface X, there exists a constant C depending only on the rank and discriminant of NS(X), such that $$\begin{aligned} \mathrm {sys}(\sigma )^2\le C\cdot \mathrm {vol}(\sigma ) \end{aligned}$$ sys ( σ ) 2 ≤ C · vol ( σ ) holds for any stability condition on $$\mathcal {D}^b\mathrm {Coh}(X)$$ D b Coh ( X ) . This is an algebro-geometric generalization of a classical systolic inequality on two-tori. We also discuss applications of this inequality in symplectic geometry.

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Section: Related Workmentioning

confidence: 98%

Systolic inequalities for K3 surfaces via stability conditions

Fan

2021

Math. Z.

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“…After this article was written and posted in arXiv.org, T. Pacini kindly informed us the relevance of [19]. We express our gratitude for this.…”

Section: Acknowledgementsmentioning

confidence: 99%

Topological invariants and Holomorphic Mappings

Greene¹,

Kim²,

Shcherbina³

2022

Comptes Rendus. Mathématique

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Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the k-sphere into the manifold are investigated. The invariants are monotonic under holomorphic mappings and strictly monotonic under certain circumstances. Applications to holomorphic maps of annular regions in C and tubular neighborhoods of compact totally real submanifolds in general in C n , n ≥ 2, are given. The contractibility of a hyperbolic domain with contracting holomorphic mapping is explained.

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Minimal distances for certain quantum product codes and tensor products of chain complexes

Zeng

Pryadko

2020

Phys. Rev. A

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Extremal Length in Higher Dimensions and Complex Systolic Inequalities

Cited by 3 publications

References 8 publications

Systolic inequalities for K3 surfaces via stability conditions

Systolic inequalities for K3 surfaces via stability conditions

Topological invariants and Holomorphic Mappings

Minimal distances for certain quantum product codes and tensor products of chain complexes

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