Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on p-forms

Comptes Rendus Mathematique - Tập 357 - Trang 180-187 - 2019
Deborah Michel1
1Laboratoire de mathématiques Raphaël-Salem, UMR 6085 CNRS–Université de Rouen, avenue de l'Université, BP 12, Technopôle du Madrillet, 76801 Saint-Étienne-du-Rouvray, France

Tài liệu tham khảo

Escobar, 1999, An isoperimetric inequality and the first Steklov eigenvalue, J. Funct. Anal., 165, 101, 10.1006/jfan.1999.3402 Escobar, 2000, A comparison theorem for the first non-zero Steklov eigenvalue, J. Funct. Anal., 178, 143, 10.1006/jfan.2000.3662 Gallot, 1975, Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne, J. Math. Pures Appl. (9), 54, 259 Guerini, 2004, Eigenvalue and gap estimates for the Laplacian acting on p-forms, Trans. Amer. Math. Soc., 356, 319, 10.1090/S0002-9947-03-03336-1 Raulot, 2011, A Reilly formula and eigenvalue estimates for differential forms, J. Geom. Anal., 22, 620, 10.1007/s12220-010-9161-0 Raulot, 2012, On the first eigenvalue of the Dirichlet-to-Neumann operator on forms, J. Funct. Anal., 262, 889, 10.1016/j.jfa.2011.10.008 Raulot, 2014, On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain, J. Geom. Phys., 77, 1, 10.1016/j.geomphys.2013.11.002 Schwarz, 1995, Hodge Decomposition—A Method for Solving Boundary Value Problems, vol. 1607