Compact isospectral sets of plane domains.
Compact isospectral sets of plane domains.
复制标题
平面域的紧凑等谱集。
DOI：
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发表时间：
1988
影响因子：
11.1
通讯作者：
Peter Sarnak
中科院分区：
文献类型：
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作者：
Brad Osgood;Ralph S. Phillips;Peter Sarnak
在C（无穷）拓扑中，二维欧几里得域的任何等谱族都是紧致的。先前，梅尔罗斯利用热不变量，建立了边界曲线曲率的C（无穷）紧性。本文用来获得域紧性的另一个成分是模空间边界附近拉普拉斯行列式的行为。
Any isospectral family of two-dimensional Euclidean domains is shown to be compact in the C(infinity) topology. Previously Melrose, using heat invariants, was able to establish the C(infinity) compactness of the curvature of the boundary curves. The additional ingredient used in this paper to obtain the compactness of the domains is the behavior of the determinant of the Laplacian near the boundary of the moduli space.