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Continuity of nonlinear eigenvalues in $CD(K,infty)$ spaces with respect to measured Gromov-Hausdorff convergence

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 نشر من قبل Jacobus Portegies
 تاريخ النشر 2017
  مجال البحث
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In this note we prove in the nonlinear setting of $CD(K,infty)$ spaces the stability of the Krasnoselskii spectrum of the Laplace operator $-Delta$ under measured Gromov-Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of $CD^*(K,N)$ metric measure spaces with uniformly bounded diameter. Additionally, we show that every element $lambda$ in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial $u$ satisfying the eigenvalue equation $- Delta u = lambda u$.



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