Abstract
We establish a quantitative isoperimetric inequality in higher codimension. In particular, we prove that for any closed (n 1)-dimensional manifold in R n+k the following inequality D() Cd 2 () holds true. Here, D() stands for the isoperimetric gap of , i.e. the deviation in measure of from being a round sphere and d() denotes a natural generalization of the Fraenkel asymmetry index of to higher codimensions.
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