New extremal domains for the first eigenvalue of the Laplacian in flat tori

79 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Solutions to overdetermined elliptic problems in nontrivial exterior domains (2016, background): “This conjecture has been answered negatively for N ≥ 3 in [25], where the third author finds a periodic perturbation of the straight cylinder BN−1 ×R that supports a periodic solution to problem (1.”
Serrin’s overdetermined problem and constant mean curvature surfaces (2013, background): “The BCN conjecture, in the case of cylindrical domains, was disproved by Sicbaldi in [23], where he provided a counterexample in the case when N ≥ 3 and f(t) = λt, λ > 0 by constructing a periodic perturbation of the cylinder BN−1 ×R which supports a bounded solution to (1.”
BIFURCATING EXTREMAL DOMAINS FOR THE FIRST EIGENVALUE OF THE LAPLACIAN (2011, methodology): “The goal of this paper is to show that these domains Ωj (introduced in [20] by the second author) belong to a smooth bifurcating family of domains, to determine their approximate shape for small bifurcation values, and to determine the bifurcation values T∗(n).”
A Rigidity Result for Overdetermined Elliptic Problems in the Plane (2015, background): “In [31] the third author gave a counterexample to that conjecture for n 3, constructing a periodic perturbation of the straight cylinder B 1 R that supports a periodic solution to problem (1.”