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»ã±¨ÌáÒª£ºThe fractional isoperimetric and isocapacitary inequalities, which compare the fractional anisotropic perimeter and Sobolev capacity with volume(s), are discussed. To fulfill the goals, I will explain the motivations, definitions and properties of the fractional anisotropic perimeter and Sobolev capacity. Moreover, I will discuss the applications to the embedding theory of functions. At last, the (log) Minkowski and reverse (log) Minkowski type inequalities are also discussed.

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