歌剧院GJMS
Masse des opérateurs GJMS
摘要：
本文推广了Habermann和Jost在Yamabe正共形类中构造正则度规的方法，该方法使用共形拉普拉斯算子的格林函数。在维数$n=2k+1$，$2k+2$，或$2k+3$中，如果第$k$个GJMS算子$P_k$允许一个格林函数，当限制于适当的共形因子选择时，其奇异性的常数项是权值为$2k-n$的共形密度.当它是正的时，它被用来在共形类中建立一个典范度量。在Paneitz-Branson算子$P_2$的情况下，在5维，6维或7维，我们显示了一个积极的结果。此外，我们还通过格林函数将它与由球极平面投影得到的流形的一个渐近不变量联系起来。
英文摘要：
This work generalizes a construction by Habermann and Jost of a canonical metric in a Yamabe-positive conformal class, which uses the Green function of the conformal Laplacian. In dimension $n=2k+1$, $2k+2$, or $2k+3$, if the $k$-th GJMS operator $P_k$ admits a Green function, the constant term of its singularity is shown to be a conformal density of weight $2k-n$, when restricted to appropriate choices of conformal factor. When it is positive, it is used to build a canonical metric in the conformal class. In the case of the Paneitz-Branson operator $P_2$, in dimension 5, 6 or 7, we show a positiveness result. In additition, we relate it to an asymptotic invariant of the manifold obtained by stereographic projection via the Green function.
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