Steklov eigenvalues of curvilinear polygons are asymptotically equal to explicit quasi-eigenvalues built from side lengths and angles, with errors tending to zero.
Heat trace asymptotics for quantum graphs
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abstract
We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admits an asymptotic expansion at t=0 with coefficients that depend on the potential in a universal way. These coefficients are spectral invariants, we compute the first few of them.
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Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons
Steklov eigenvalues of curvilinear polygons are asymptotically equal to explicit quasi-eigenvalues built from side lengths and angles, with errors tending to zero.