Extremal metrics for Laplace eigenvalues in perturbed conformal classes
classification
🧮 math.DG
math.AP
keywords
conformalextremalclasseslaplacemetricsperturbedallowsarguments
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We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain perturbed harmonic maps with constant density.
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