Heat kernels and Green’s functions on limit spaces

By Yu Ding. 2002

89 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6196159369b9f3bae14ce91c8ac32a128baca2ad

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Ricci curvature and $L^p$-convergence (2012, background): “See also [18, 32, 33, 34, 35] for a convergence of heat kernels.”
Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K, N)$-spaces (2017, methodology): “For suchmetric measure spaces,Weyl’s lawwas proven in [19] byDing.”
Local spectral convergence in RCD∗(K,N) spaces (2017, background): “igenvalue λ for the Dirichlet problem on BR(p) if Z BR(p) Γ(f,g)dm= λ Z BR(p) fgdm ∀g ∈ H1,2 0 (BR(p),d,m), (1.5) where Γ is the carré du champ operator associated to the metric measure structure. In [D02] the question whether the limit function of k-eigenvalues still satisﬁes the Dirichlet boundary”
Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows (2018, result): “s locally like the distance raised to the power 2 − n(see [Au98, Chapter 4]). The comparison is also global on a non compact manifold with nonnegative Ricci curvature and Euclidean volume growth (see [D02]) and, in our previous work [BrSe18], we extended these results to Ahlfors regular RCD(K,N) met”
Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below (2018, methodology): “e have sup 1 2B\S u≤ CkukL2(B) for a constant Cdepending on the dimension and asymptotic volume ratio of X. Proof. Given y∈ 1 2B\ S, let Ht(x,y) be the heat kernel on Xsatisfying ∂tHt = ∆xHt(see Ding [9] for details on the heat kernel on tangent cones). In addition let ηbe a cutoﬀ function such that”