We prove an analogue of the 4-dimensional local Viterbo conjecture for the higher Ekeland-Hofer capacities: on the space of 4-dimensional smooth star-shaped domains of unitary volume, endowed with the C3 topology, the local maximizers of the k-th Ekeland-Hofer capacities are those domains symplectomorphic to suitable rational ellipsoids.
On the local maximizers of higher capacity ratios
Baracco, Luca;Bernardi, Olga;
2024
Abstract
We prove an analogue of the 4-dimensional local Viterbo conjecture for the higher Ekeland-Hofer capacities: on the space of 4-dimensional smooth star-shaped domains of unitary volume, endowed with the C3 topology, the local maximizers of the k-th Ekeland-Hofer capacities are those domains symplectomorphic to suitable rational ellipsoids.
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