Geodesic
Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1

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Zbl
We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.
Mots-clés : Eigenvalues of the Laplacian, convexity, Ham Sandwich Theorem 
Funano, Kei. Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a19/
@article{AGMS_2016_4_1_a19,
     author = {Funano, Kei},
     title = {Applications of the {{\textquoteleft}Ham} {Sandwich} {Theorem{\textquoteright}} to {Eigenvalues} of the {Laplacian}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2016},
     volume = {4},
     number = {1},
     zbl = {1354.58024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a19/}
}
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