The Structure of Complete Manifolds With Weighted Poincaré Inequality and Minimal Hypersurfaces

Fu, Hai-Ping; Zhen-qi, LI

doi:10.1142/s0129167x10006550

Cited by 8 publications

(7 citation statements)

References 9 publications

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“…Actually, it improves the original version. This generalization of Shen-Zhou result has been recently observed also by H. Fu and Z. Li, [19]. However, their approach is less direct than ours and relies on a structure theorem by Anderson, [1].…”

Section: Back To Minimal Hypersurfacessupporting

confidence: 74%

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REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS

Pigola

Veronelli

2012

Int. J. Math.

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Abstract. We survey some L p -vanishing results for solutions of Bochner or Simons type equations with refined Kato inequalities, under spectral assumptions on the relevant Schrödinger operators. New aspects are included in the picture. In particular, an abstract version of a structure theorem for stable minimal hypersurfaces of finite total curvature is observed. Further geometric applications are discussed. Introduction and some vanishing resultsThis paper originates from an attempt to understand the abstract content of a structure theorem for stable minimal hypersurfaces of finite total scalar curvature.(ii) The "stability operator" L = −∆ − |II| 2 has non-negative spectrum.Then, |II| ≡ 0, that is, f (M ) is an affine m-plane .

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Section: Back To Minimal Hypersurfacessupporting

confidence: 74%

“…We claim that they are everywhere distinct. Indeed, using (19) and arguing as in Section 5, we see that v = |Ric| Thus |Ric| > 0 and this forces µ = −µ/ (m − 1), as claimed. Now, we observe that Ric is not parallel.…”

Section: It Follows Thatmentioning

confidence: 56%

REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS

Pigola

Veronelli

2012

Int. J. Math.

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“…then (M 4 , g) is anti-self-dual (resp., self-dual). [4,19,20]). In order to prove Theorem 1.1, we also need the following proof of Theorem E.…”

Section: Four Manifolds With Half Harmonic Weyl Tensormentioning

confidence: 99%

Four-manifolds with positive Yamabe constant

2018

Pacific J. Math.

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We refine Theorem B due to Gursky [26]. As applications, we give some rigidity theorems on four-manifolds with postive Yamabe constant. In particular, these rigidity theorems are sharp for our conditions have the additional properties of being sharp. By this we mean that we can precisely characterize the case of equality. We prove some classification theorems of four manifolds according to some conformal invariants (see Theorems 5.1, 1.3 and 1.6), which reprove and generalize the conformally invariant sphere theorem of Chang-Gursky-Yang [11], i.e., Theorem D.2000 Mathematics Subject Classification. Primary 53C21; Secondary 53C20.

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“…Finally, since Ric is a Codazzi tensor the refined Kato inequality Assume also that M = R m , for otherwise there is nothing to prove. Application of Theorem 5 (ii) yields the equality in (18), i.e., (19) |Ric|…”

Section: 2mentioning

confidence: 99%

Remarks on $L^{p}$-vanishing results in geometric analysis

Pigola¹,

Veronelli²

2010

Preprint

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We survey some L p -vanishing results for solutions of Bochner or Simons type equations with refined Kato inequalities, under spectral assumptions on the relevant Schrödinger operators. New aspects are included in the picture. In particular, an abstract version of a structure theorem for stable minimal hypersurfaces of finite total curvature is observed. Further geometric applications are discussed.

show abstract

The Structure of Complete Manifolds With Weighted Poincaré Inequality and Minimal Hypersurfaces

Cited by 8 publications

References 9 publications

REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS

REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS

Four-manifolds with positive Yamabe constant

Remarks on $L^{p}$-vanishing results in geometric analysis

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The Structure of Complete Manifolds With Weighted Poincaré Inequality and Minimal Hypersurfaces

Cited by 8 publications

References 9 publications

REMARKS ON Lp-VANISHING RESULTS IN GEOMETRIC ANALYSIS

REMARKS ON Lp-VANISHING RESULTS IN GEOMETRIC ANALYSIS

Four-manifolds with positive Yamabe constant

Remarks on $L^{p}$-vanishing results in geometric analysis

Contact Info

Product

Resources

About

REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS

REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS