BEST ISOPERIMETRIC CONSTANTS FOR (H 1, BMO)-NORMAL CONFORMAL METRICS ON R n, n ≥ 3 †
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چکیده
Alice Chang’s Question: A very general question is to ask “What is the geometric content of Q-curvature?” For example, we know that one can associate the scalar curvature with the conformally invariant constant called the “Yamabe constant”. When this constant is positive, it describes the best constant (in a conformally invariant sense) of the Sobolev embedding of W 1,2 into L space; this in itself can be viewed as a W 1,2 version of the isoperimetric inequality. It would be interesting to know if Q-curvature, or the conformally invariant quantity ∫
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TOWARD BEST ISOPERIMETRIC CONSTANTS FOR (H 1, BMO)-NORMAL CONFORMAL METRICS ON R n, n ≥ 3 †
Alice Chang’s Question: A very general question is to ask “What is the geometric content of Q-curvature?” For example, we know that one can associate the scalar curvature with the conformally invariant constant called the “Yamabe constant”. When this constant is positive, it describes the best constant (in a conformally invariant sense) of the Sobolev embedding of W 1,2 into L space; this in it...
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تاریخ انتشار 2008