Deficit in the Trudinger-Moser inequality quadratically bounds distance to optimizers on bounded domains in the plane when the exponential growth rate is small or the domain is a round disk.
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Quantitative stability for the Trudinger-Moser inequality
Deficit in the Trudinger-Moser inequality quadratically bounds distance to optimizers on bounded domains in the plane when the exponential growth rate is small or the domain is a round disk.