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The volume-condition extension of the strong maximum principle

Let MM, β\beta, θ\theta, ρ\rho, u u, bb, and the conditions defining the range

andand

be as in Theorem

. **The volume-condition extension of the strong maximum principle.** In that setting, the full $(\mathrm{SMP}_\infty)$ holds if the range

is replaced by

.ThestatementispresentedasaconjecturalextensionofTheorem. The statement is presented as a conjectural extension of Theorem

, but the supplied text gives no resolution or further context.

Sources & referencesView supporting material

Primary source

Bruno Bianchini, Luciano Mari, Patrizia Pucci and Marco Rigoli, “On the interplay among maximum principles, compact support principles and Keller-Osserman conditions on manifolds”, arXiv:1801.02102 (2018).

elliptic-operatorsmaximum-principlesriemannian-geometry

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