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Gromov Width

The Gromov width of a symplectic manifold is the supremum of the capacities of standard open symplectic balls that embed smoothly into it while preserving the symplectic form. In standard coordinates (q,p) in R^n×R^n, the ball of capacity c is

B^(2n)(c)={(q,p):pi(||q||^2+||p||^2)<c}.

Its Euclidean radius is sqrt(c/pi), and its volume is c^n/n!. For an open subset U of standard symplectic space, its width is

c_G(U)=sup{c>0:B^(2n)(c) admits a smooth symplectic embedding into U}.

See also

Symplectic Ball Packing, Symplectic Form, Symplectic Manifold

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References

Schlenk, F. "Symplectic Embedding Problems, Old and New." Bull. Amer. Math. Soc. 55, 139-182, 2018. https://doi.org/10.1090/bull/1587.

Cite this as:

Weisstein, Eric W. "Gromov Width." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GromovWidth.html

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