Maximum Principles On Riemannian Manifolds And Applications

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Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields (2017, background): “perator ∆U (respectively, ∆f) on Mif for any u∈ C2(M) with u∗ = supMu<∞ and for each γ<u∗ we have inf Ωγ ∆Uu≤ 0, respectively inf Ωγ ∆fu≤ 0), where Ωγ = {x∈ M: u(x) >γ}. From Theorem 3.11 of [42] we know that the validity of the weak maximum principle for the operator ∆f is equivalent to it”
On the scalar curvature of constant mean curvature hypersurfaces in space forms (2009, methodology): “S. Pigola, M. Rigoli and A.G. Setti, Maximum principles on Riemannian manifolds and applications, Memoirs Amer.”
Ricci almost solitons (2010, methodology): “Furthermore, reasoning as in [25] we have”
Remarks on non-compact gradient Ricci solitons (2009, methodology): “for every t > 0 and for every x ∈M , [16].”