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Energy Quantization for Yamabe's problem in Conformal Dimension

Fethi Mahmoudi
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Abstract

T. Riviere proved an energy quantization for Yang-Mills fields defined on n-dimensional Riemannian manifolds, when $n$ is larger than the critical dimension 4. More precisely, he proved that the defect measure of a weakly converging sequence of Yang-Mills fields is quantized, provided the $W^{2,1}$ norm of their curvature is uniformly bounded. In the present paper, we prove a similar quantization phenomenon for the Yamabe problem in a bounded domain $Ω$ of $R^n$.

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Fethi Mahmoudi. 2006-09-04. Energy Quantization for Yamabe's problem in Conformal Dimension. https://arxiv.org/abs/math/0609103

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