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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{liu2026sharp,
  title = {{Sharp Signed Mass and Rigidity for Critical Finsler--Liouville Equations}},
  author = {Yanjun Liu and Zhongwei Tang and Heming Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26930},
  eprint = {2610.26930},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26930},
}
RIS
TY  - UNPB
TI  - Sharp Signed Mass and Rigidity for Critical Finsler--Liouville Equations
AU  - Yanjun Liu
AU  - Zhongwei Tang
AU  - Heming Wang
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.26930
UR  - https://arxiv.org/abs/2610.26930
AB  - 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.
ER  -