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Disquisitiones Mathematicae
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Matheus' Weblog
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Disquisitiones Mathematicae
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2026-03-02 10:30:38
raw text
Disquisitiones Mathematicae | Matheus’ Weblog Disquisitiones Mathematicae Matheus’ Weblog Posted by: matheuscmss | May 3, 2021 Spectral rigidity of almost circular ellipses (after Hezari–Zelditch) In 1966, M. Kac wrote a famous article asking whether Can one hear the shape of drum? : mathematically speaking, one wants to reconstruct (up to isometries) a domain from the knowledge of the spectrum of its Laplacian. In his article, M. Kac showed that one can hear the shape of a disk because of the following two facts: the area and the perimeter of a smooth domain are determined by the eigenvalues of its Laplacian via the asymptotics of the trace of the heat operator : the isoperimetric inequality says that we can recognise the disk from its perimeter and area: indeed, any smooth domain satisfies , and the equality holds if and only if is isometric to a disk of radius . (In particular, a smooth domain with the same Laplace eigenvalues of has a...
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60 - mathscinet.ams.org, carlos.matheus.perso.math.cnrs.fr, him.uni-bonn.de, math.u-bordeaux.fr, conferences.cirm-math.fr, iecl.univ-lorraine.fr, ora.ox.ac.uk, bourbaki.ens.fr, mathscinet-ams-org.ezproxy.math.cnrs.fr, mat.ufc.br, i2m.univ-amu.fr, blogs.ethz.ch, mat.uc.cl
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