On a paper of Berestycki–Hamel–Rossi and its relations to the weak maximum principle at infinity, with applications

Magliaro, Marco; Mari, Luciano; Rigoli, Marco

doi:10.4171/RMI/1009

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Revista Matemática Iberoamericana

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Volume 34, Issue 2, 2018, pp. 915–936

DOI: 10.4171/RMI/1009

Published online: 2018-05-28

On a paper of Berestycki–Hamel–Rossi and its relations to the weak maximum principle at infinity, with applications

Marco Magliaro^[1], Luciano Mari^[2] and Marco Rigoli^[3]

(1) Universidade Federal do Ceará, Fortaleza, Brazil
(2) Scuola Normale Superiore, Pisa, Italy
(3) Università di Milano, Italy

The aim of this paper is to study a new equivalent form of the weak maximum principle for a large class of differential operators on Riemannian manifolds. This new form has been inspired by the work of Berestycki, Hamel and Rossi for trace operators, and allows us to shed new light on it and to introduce a new sufficient bounded Khas’minskii type condition for its validity. We show its effectiveness by applying it to obtain some uniqueness results in a geometric setting.

Keywords: Weak maximum principle, Khas’minskii type conditions, Lichnerowicz equation, Ricci solitons

Magliaro Marco, Mari Luciano, Rigoli Marco: On a paper of Berestycki–Hamel–Rossi and its relations to the weak maximum principle at infinity, with applications. Rev. Mat. Iberoam. 34 (2018), 915-936. doi: 10.4171/RMI/1009