Skip to content
DraconiticResearch
Search Sources API
186,125 studies31 sourcesUpdated 43 min ago
PreprintarXiv licencearXiv

Boundary Cases of the J-Equation: Divisorial Rigidity and a Global C0 Estimate

  • Jixiang Fu
  • Ziyi Zhang
Open at sourcePDFDOICite

Abstract

We study two boundary cases of the stability condition for the J-equation. First, under the J-semistable condition, we show that the destabilizing prime divisors form an exceptional family in the sense of Boucksom, with a uniform numerical gap away from them. The related modified nef estimate can remove the J-big assumption in Liu's work~\cite{Liu2026Boundary}. Second, under the smooth boundary cone condition, we obtain a uniform global C0 estimate for solutions of the approximating twisted J-equations. As a consequence, we construct a bounded-potential Bedford--Taylor solution of the J-equation, which is smooth outside the destabilizing prime divisors.

Related

  1. Divisorial Rigidity and Regularity of Boundary Cases for the Supercritical LYZ Equation
    Jixiang Fu, Shing-Tung Yau, Dekai Zhang +1
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. A rigidity result for a global vectorial free boundary problem with a linear datum
    Giovanni Siclari, Bozhidar Velichkov
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. The critical boundary value for a nonlinear Schrödinger equation in a half-space: rigidity and dimensional transition
    Phuong Le
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Rigidity and volume pinching for the sharp gradient estimate in positive Ricci curvature
    Junyoung Kim, Jiewon Park
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  5. A geometric rigidity estimate for codimension-1 immersions into spheres
    Siran Li, Isaac Newell
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{fu2026boundary,
  title = {{Boundary Cases of the $J$-Equation: Divisorial Rigidity and a Global $C^0$ Estimate}},
  author = {Jixiang Fu and Ziyi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29736},
  eprint = {2608.29736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29736},
}
RIS
TY  - UNPB
TI  - Boundary Cases of the J-Equation: Divisorial Rigidity and a Global C^0 Estimate
AU  - Jixiang Fu
AU  - Ziyi Zhang
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29736
UR  - https://arxiv.org/abs/2608.29736
AB  - We study two boundary cases of the stability condition for the J-equation. First, under the J-semistable condition, we show that the destabilizing prime divisors form an exceptional family in the sense of Boucksom, with a uniform numerical gap away from them. The related modified nef estimate can remove the J-big assumption in Liu's work~\cite{Liu2026Boundary}. Second, under the smooth boundary cone condition, we obtain a uniform global C^0 estimate for solutions of the approximating twisted J-equations. As a consequence, we construct a bounded-potential Bedford--Taylor solution of the J-equation, which is smooth outside the destabilizing prime divisors.
ER  -