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arXiv · 2610.26930

Sharp Signed Mass and Rigidity for Critical Finsler--Liouville Equations

Yanjun Liu·Zhongwei Tang·Heming Wang
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Abstract

We study bounded-above entire solutions of critical Finsler--Liouville equations with a possibly sign-changing prescribed function and finite absolute mass. Under a lower cone-growth condition, we establish a sharp signed-mass bound without upper growth or monotonicity assumptions. With an additional growth condition, annular compactness for a sequence of dilations yields Pohozaev boundary limits and rigidity for radially nonincreasing prescribed functions. Explicit examples show that the rigidity threshold is optimal. In the Euclidean plane, the mass estimate also gives a sharp obstruction to completeness.

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Yanjun Liu, Zhongwei Tang, Heming Wang. 2026-10-17. Sharp Signed Mass and Rigidity for Critical Finsler--Liouville Equations. https://arxiv.org/abs/2610.26930

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