Closed generalized Einstein manifolds with positive isotropic curvature

Hwang, Seungsu; Santos, Marcelo Soares Teles; Yun, Gabjin

doi:10.48550/arxiv.2108.10675

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…The Black Hole Uniqueness Theorem for three-dimensional static solutions with positive scalar curvature and the Besse Conjecture for solutions to the Critical Point Equation are two very famous and related open problems in contemporary geometric analysis. Very recently, some very remarkable advances have been claimed on both of these problems in a series of papers [1,2,3,6,7,8]. In this short note, we point out an issue in the approach proposed in the above mentioned papers, providing counterexamples.…”

Section: Introductionmentioning

confidence: 86%

Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

Borghini¹,

Mazzieri²

2023

Preprint

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In [3] an estimate for suitable skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: most notably, it has been employed to propose a proof of a Black Hole Uniqueness Theorem for vacuum static spacetimes with positive scalar curvature [6] and in connection with the Besse Conjecture [8]. In the present note we point out an issue in the argument proposed in [3] and we provide a counterexample to the estimate.

show abstract

Section: Introductionmentioning

confidence: 86%

Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

Borghini¹,

Mazzieri²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The Black Hole Uniqueness Theorem for three-dimensional static solutions with positive scalar curvature and the Besse conjecture for solutions to the critical point equation are two very famous and related open problems in contemporary geometric analysis. Very recently, some very remarkable advances have been claimed on both of these problems in a series of papers [1][2][3][6][7][8]. In this short note, we point out an issue in the approach proposed in the above-mentioned papers, providing counterexamples.…”

Section: Introductionmentioning

confidence: 88%

“…In both cases, the classification follows easily. The same strategy is adopted in [6], 1 where this time the differential 2-form ω is defined as…”

Section: Introductionmentioning

confidence: 99%

Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

Borghini

Mazzieri

2023

Ann Glob Anal Geom

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In Hwang and Yun (Ann Glob Anal Geom 62(3):507–532, 2022), an estimate for skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: Most notably, it has been employed to propose a proof of a Black Hole Uniqueness Theorem for vacuum static spacetimes with positive scalar curvature (Xu and Ye in Invent Math 33(2):64, 2022) and in connection with the Besse conjecture (Yun and Hwang in Critical point equation on three-dimensional manifolds and the Besse conjecture). In the present note, we point out an issue in the argument proposed in Hwang and Yun (Ann Glob Anal Geom 62(3):507–532, 2022) and we provide a counterexample to the estimate.

show abstract

Closed generalized Einstein manifolds with positive isotropic curvature

Cited by 2 publications

References 12 publications

Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

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