COMPACT MANIFOLDS WITH FIXED BOUNDARY AND LARGE STEKLOV EIGENVALUES
COMPACT MANIFOLDS WITH FIXED BOUNDARY AND LARGE STEKLOV EIGENVALUES
复制标题
DOI：
10.1090/proc/14426
复制
发表时间：
2019-09-01
影响因子：
1
通讯作者：
Girouard, Alexandre
中科院分区：
文献类型：
--
作者：
Colbois, Bruno;El Soufi, Ahmad;Girouard, Alexandre
设（M，g）是一个带边界的紧致黎曼流形.设B > 0为其边界的连通分支数。对于维数>= 3的流形，我们证明了对j = B + 1，利用保角扰动可以得到任意大的Steklov本征值sigma（j）（M，e（delta）g）δ是C-无穷大（M）的一个元素，它被支撑在边界的一个薄邻域中，在边界上δ = 0.对于j
Let (M, g) be a compact Riemannian manifold with boundary. Let b > 0 be the number of connected components of its boundary. For manifolds of dimension >= 3, we prove that for j = b + 1 it is possible to obtain an arbitrarily large Steklov eigenvalue sigma(j)(M, e(delta)g) using a conformal perturbation delta is an element of C-infinity(M) which is supported in a thin neighbourhood of the boundary, with delta = 0 on the boundary. For j