A Surgery Result for the Spectrum of the Dirichlet Laplacian

Dorin Bucur, Dario Mazzoleni
2015 SIAM Journal on Mathematical Analysis  
In this paper we give a method to geometrically modify an open set such that the first k eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure remains constant, and both perimeter and diameter decrease below a certain threshold. The key point of the analysis relies on the properties of the shape subsolutions for the torsion energy.
doi:10.1137/140992448 fatcat:5cdw5jutqjh55jnxmxngm5oteu