Compact isospectral sets of surfaces
نویسندگان
چکیده
منابع مشابه
Compact isospectral sets of plane domains.
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 boun...
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0 κ0κ1 1 · · ·κ αk−1 k−1 ds , k ≥ 3 . Here ck 6= 0 and the sum, which is finite, consists of lower order terms in the sense that αk−1 ≤ 2. The bk+1 therefore bound the corresponding Sobolev norms on κ and the compactness, in the C∞ topology on κ, of the set of domains with a fixed spectrum follows. The coefficients a0, a1, a2, a3, b0, b1, b2 have already been computed, see L. Smith [5] and the ...
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In this paper we study sets of surfaces which are isospectral with respect to the Laplace-Beltrami operator. More specifically, for closed surfaces (compact, no boundary) we consider a fixed surface and the family of metrics on that surface having a given Laplace spectrum, whereas for surfaces with boundary we confine our study to the class of simply connected planar domains all having the same...
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In memory of Hubert Pesce In this paper, we investigate the following question: to what extent is there a converse to the Theorem of Sunada Su] in the context of graphs? Our experience in dealing with the question, \Can one hear the shape of a drum?" is that the many facets of this question turn out to be surprisingly delicate. The present instance is no exception. We will rst present a partial...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1988
ISSN: 0022-1236
DOI: 10.1016/0022-1236(88)90071-7