Fundamental Gap of Convex Domains in the Spheres
Chenxu He, Guofang Wei, Qi S. Zhang
Abstract
S. Seto, L. Wang, and G. Wei proved that the gap between the first two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as large as that for an associated operator on an interval with the same diameter, provided that the domain has the diameter at most $\pi/2$. In this paper, we extend Seto-Wang-Wei's result to convex domains in the unit sphere with diameter less than $\pi$.
Topics & Concepts
MathematicsUnit sphereRegular polygonSPHERESDomain (mathematical analysis)Eigenvalues and eigenvectorsUnit (ring theory)Operator (biology)Convex domainMathematical analysisDirichlet distributionCombinatoricsPure mathematicsGeometryPhysicsBiochemistryMathematics educationRepressorGeneAstronomyBoundary value problemTranscription factorChemistryQuantum mechanicsAnalytic and geometric function theoryAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential Equations