4 problems

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Conformal-invariant extension of the rigidity theorem and lower bound for Weyl curvature
The conformal-invariant extension conjecture. Theorem t-rigidity and Corollary c-asf hold assuming only one of the conformal invariant conditions
Conjectureopenconformal-geometry riemannian-geometry weyl-curvaturearXiv posted 2 days ago
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Kobayashi's Weyl functional conjecture for $S^2\times S^2$
Kobayashi's conjecture. The infimum of the Weyl functional on $S^2\times S^2$ is achieved by the Kähler–Einstein metric arising as the Riemannian product of two round $2$ -spheres o…
Conjectureopenfour-manifolds kahler-geometry weyl-curvaturearXiv posted 2 days ago
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Hermitian Einstein characterization of absolute Weyl-functional minimizers
Hermitian Einstein minimizer conjecture. The conformal class $[g]$ is an absolute minimizer of $\mathscr{W}$ . Moreover, for the given $M$ , every absolute minimizer arises from a me…
Conjectureopeneinstein-metrics four-manifolds weyl-curvaturearXiv posted 2 days ago
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Positive Kähler–Einstein metrics as absolute Weyl-functional minimizers
Absolute-minimizer conjecture. In real dimension $4$ , positive Kähler–Einstein metrics are absolute minimizers of the Weyl functional among all conformal classes on the fixed manif…
Conjectureopenfour-manifolds kahler-einstein-metrics weyl-curvaturearXiv posted 2 days ago

Conformal-invariant extension of the rigidity theorem and lower bound for Weyl curvature