Symplectic embeddings of polydisks

By Larry Guth. 2007

82 citations recorded by the source corpus.

If P and P′ are symplectic polydisks of radii R1≤...≤Rn and R1′≤...≤Rn′, respectively, then we prove that P symplectically embeds in P′ provided that C(n)R1≤R1′ and C(n)R1...Rn≤R1′...Rn′. Up to a constant factor, these conditions are optimal.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0cdefd1639821d6dab3b23fafdd6e5d01dfe8907

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

THE SHARP ENERGY-CAPACITY INEQUALITY (2008, background): “1]; in fact, recent constructions in [7] show that, for some constant κ > 0, one can take as large as κr−2).”
The Hofer conjecture on embedding symplectic ellipsoids (2010, result): “In [5] Hind–Kerman improved Guth’s embedding method to show that E(1, R, . . . , R) embeds in E(a, a,R2, . . . , R2) whenever a > 3, but found an obstruction when a 3.”
Symplectic embedding problems, old and new (2017, methodology): “This “third revolution” was instigated by two ingenious constructions by Guth [51] and McDuff [79].”
Symplectic embeddings of 4‐dimensional ellipsoids (2008, unknown): “Acknowedgements. I was inspired to think about this problem by discussions with Hofer and Guth, who in [ 7 ] recently solved (in the negative) Hofer’s question about the existence of higher dimensional capacities.”
Symplectic embeddings into four‐dimensional concave toric domains (2013, background): “Another example is that if there is a symplectic embedding from P (1, 2) into the ball B(c), then both ECH capacities and Ekeland–Hofer capacities only imply that c 2; but in fact it was recently shown by Hind–Lisi [3] that c 3.”
The embedding capacity of 4-dimensional symplectic ellipsoids (2009, background): “(See Hind–Kerman [9] for a more precise version of Guth’s result.)”