Eigenvalues and eigenfunctions of metric measure manifolds

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An optimal anisotropic Poincaré inequality for convex domains (2011, methodology): “Particularly, many problems related to the first eigenvalue of the anisotropic Laplacian have already been considered in [Belloni et al. 2003; Ge and Shen 2001; Kawohl 2011; Ohta 2009; Wang and Xia 2011a].”
A sharp lower bound for the first eigenvalue on Finsler manifolds (2011, methodology): “ive functions η∈ Wc1,2(M) T L∞(M). 3. Proofof Theorem 1.1 We ﬁrst remark that a weak eigenfunction u∈ W1,2(M) of Finsler-Laplacian deﬁned in (1) has regularity that u∈ C1,α(M) T W2,2(M) T C∞(Mu) (see [6]). Let us recall the 1-D models LK,N described in [3]. Let K∈ Rand N∈ (1,∞]. (i) For K>0 and 1”
Heat flow on Finsler manifolds (2008, result): “ion. Formulation of results and proofs follow classical lines. For the elliptic case, similar results have already been derived by Shen [Sh2] and by Belloni, Kawohl and Juutinen [BKJ]. See also [Di], [GS]. Throughout the chapter, the assumptions (1.2) and (2.1) will be in force. 14 Deﬁnition 4.1 Giv”