Geometric Aspects of Functional Analysis pp 137-149 | Cite as

# A Remark on Projections of the Rotated Cube to Complex Lines

## Abstract

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.

## Notes

### Acknowledgements

The authors would like to thank the anonymous referee for helpful comments and remarks, and in particular for his/her suggestion to elaborate more on the symplectic topology background which partially served as a motivation for the current note. The second-named author was partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, starting grant No. 637386, and by the ISF grant No. 1274/14.

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