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The volume-condition extension of the strong maximum principle

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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.

References

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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