4 problems

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Anderson's conjecture on cusp formation on the 4-ball
Anderson's cusp-formation conjecture. Cusp formation is not possible on the $4$ -ball.
Conjectureopengeometric-analysis metric-degeneration poincare-einstein-metricsarXiv posted 2 days ago
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SYZ conjecture on metric degeneration to the base
Let $\\{(X_{\hbar},\omega_{\hbar})\\}_{\hbar>0}$ be a family of Kähler manifolds approaching the large complex structure limit, with base polytope $P$ and a rescaled Kähler metric…
Conjectureopenmetric-degeneration mirror-symmetry special-lagrangian-fibrationsarXiv posted 2 days ago
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Small-angle metric degeneration conjecture for classes $(\aleph)$ and $(\beth)$
Small-angle metric degeneration conjecture. As $\beta$ tends to zero, $(S,C,\omega_\beta)$ converges in an appropriate sense to a generalized Kähler–Einstein metric $\omega_\infty$ …
Conjectureopenkahler-einstein-metrics log-del-pezzo-surfaces metric-degenerationarXiv posted 2 days ago
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Family SYZ degeneration conjecture for Calabi–Yau varieties
Consider a family of Calabi–Yau varieties undergoing a large complex degeneration, with the associated SYZ fibrations and metric degeneration. Family SYZ degeneration conjecture. S…
Conjecturesolvedcalabi-yau-varieties metric-degeneration syz-mirror-symmetryarXiv posted 2 days ago

Anderson's conjecture on cusp formation on the 4-ball