论文标题
在父亲XU归一化下形成条状拉普拉斯的极端特征值
Extremal Eigenvalues Of The Conformal Laplacian Under Sire-Xu Normalization
论文作者
论文摘要
令$（m^n，g）$为dimension $ n \ ge 3 $的封闭式riemannian歧管。我们研究了$ k $ -th eigenvalue函数$ \ tilde g \ in [g] \mapstoλ_k（l _ {\ tilde g}）$ in [g] \ mapstoλ_k（\ tilde g}）$ s sire-xu提出的非数量归一化。我们讨论了在这种归一化下存在极端特征值的必要条件。另外，当$ k = 1 $时，我们讨论了一般存在问题。
Let $(M^n,g)$ be a closed Riemannian manifold of dimension $n\ge 3$. We study the variational properties of the $k$-th eigenvalue functional $\tilde g\in[g] \mapsto λ_k(L_{\tilde g})$ under a non-volume normalization proposed by Sire-Xu. We discuss necessary conditions for the existence of extremal eigenvalues under such normalization. Also, we discuss the general existence problem when $k=1$.
