Zobrazeno 1 - 10 of 52 pro vyhledávání: '"Pierre Bérard"'
1
Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip
Autor: Pierre Bérard, Bernard Helffer, Rola Kiwan
Publikováno v: Portugaliae Mathematica
Portugaliae Mathematica, European Mathematical Society Publishing House, 2021, 78 (1), pp.1--41
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23269f1b4be533287c7954d7dde5b771
https://doi.org/10.4171/pm/2059
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2
One can't hear orientability of surfaces
Autor: David L. Webb, Pierre Bérard
Publikováno v: Mathematische Zeitschrift
Mathematische Zeitschrift, Springer, 2021, https://doi.org/10.1007/s00209-021-02758-y
The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other non-orientable. For thi
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fba22fda5dd1b9d2cdbad7f61d3b635
https://hal.archives-ouvertes.fr/hal-02937342/file/BW2020-08-26.pdf
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3
On Courant’s Nodal Domain Property for Linear Combinations of Eigenfunctions Part II
Autor: Pierre Bérard, Bernard Helffer
Publikováno v: Springer Proceedings in Mathematics & Statistics ISBN: 9783030684891
According to Courant's theorem, an eigenfunction as\-sociated with the $n$-th eigenvalue $\lambda_n$ has at most $n$ nodal domains. A footnote in the book of Courant and Hilbert, states that the same assertion is true for any linear combination of ei
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::0d993cd98809a121c78afc6aef6d2ba8
https://doi.org/10.1007/978-3-030-68490-7_4
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4
Elektronická kniha
L’exploration de La Pérouse (1785-88) : rendue publique en 1797 par le général Millet Mureau
Autor: Pierre Bérard
L'expédition était une volonté de Louis XVI, « roi-géographe », lecteur des voyages de Cook. Il l'a confiée à La Pérouse, soucieux de la santé de ses équipages, avec un esprit ouvert sur le monde. On a reçu à Versailles 3 ans de rapports
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5
Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders
Autor: Rola Kiwan, Bernard Helffer, Pierre Bérard
Publikováno v: Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2022, 150, pp.439--453
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::913c92bb7f149e3007dc0d3e7acdb8f1
https://hal.archives-ouvertes.fr/hal-02937338
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8
Minimal hypersurfaces in $$\mathbb {H}^n \times \mathbb {R}$$ H n × R , total curvature and index
Autor: Pierre Bérard, Ricardo Sa Earp
Publikováno v: Bollettino dell'Unione Matematica Italiana. 9:341-362
In this paper, we consider minimal hypersurfaces in the product space $$\mathbb {H}^n \times \mathbb {R}$$ . We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal h
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::73c031f127d3d24cd9001cf205e44378
https://doi.org/10.1007/s40574-015-0050-0
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9
The weak Pleijel theorem with geometric control
Autor: Pierre Bérard, Bernard Helffer
Publikováno v: Journal of Spectral Theory
Journal of Spectral Theory, European Mathematical Society, 2016, 6 (4), pp.717--733
Let $\Omega\subset \mathbb R^d\,, d\geq 2$, be a bounded open set, and denote by $\lambda\_j(\Omega), j\geq 1$, the eigenvalues of the Dirichlet Laplacian arranged in nondecreasing order, with multiplicities. The weak form of Pleijel's theorem states
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e60eee4d615c466d16aed5c0c8579044
https://doi.org/10.4171/jst/138
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10
Sturm's theorem on the zeros of sums of eigenfunctions: Gelfand's strategy implemented
Autor: Bernard Helffer, Pierre Bérard
Publikováno v: Moscow Mathematical Journal
Moscow Mathematical Journal, Independent University of Moscow 2020, 20 (1), pp.1--25
In the second section "Courant-Gelfand theorem" of his last published paper (Topological properties of eigenoscillations in mathematical physics, Proc. Steklov Institute Math. 273 (2011) 25--34), Arnold recounts Gelfand's strategy to prove that the z
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59875ab2e88ccc5c1a5f8c18f87da644
http://arxiv.org/abs/1807.03990
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