The space of contractible simple loops of fixed area on compact oriented surfaces has infinite L^p-diameter under the action of area-preserving diffeomorphisms.
Hofer’s metric on the space of diameters.J
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The $L^p$-diameter of the space of contractible loops
The space of contractible simple loops of fixed area on compact oriented surfaces has infinite L^p-diameter under the action of area-preserving diffeomorphisms.