Blow-up examples for the Yamabe problem

Fernando C. Marques

doi:10.1007/s00526-009-0233-6

Blow-up examples for the Yamabe problem

Fernando C. Marques

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold (Mⁿ, g) blow-up at a point p M, then all derivatives of the Weyl tensor W_g of g, of order less than or equal to, vanish at p M. In this paper, we will construct smooth counterexamples to the Weyl Vanishing Conjecture for any n ≥ 25.

Original language	English (US)
Pages (from-to)	377-397
Number of pages	21
Journal	Calculus of Variations and Partial Differential Equations
Volume	36
Issue number	3
DOIs	https://doi.org/10.1007/s00526-009-0233-6
State	Published - Oct 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00526-009-0233-6

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abstract = "It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold (Mn, g) blow-up at a point p M, then all derivatives of the Weyl tensor Wg of g, of order less than or equal to, vanish at p M. In this paper, we will construct smooth counterexamples to the Weyl Vanishing Conjecture for any n ≥ 25.",

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N2 - It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold (Mn, g) blow-up at a point p M, then all derivatives of the Weyl tensor Wg of g, of order less than or equal to, vanish at p M. In this paper, we will construct smooth counterexamples to the Weyl Vanishing Conjecture for any n ≥ 25.

AB - It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold (Mn, g) blow-up at a point p M, then all derivatives of the Weyl tensor Wg of g, of order less than or equal to, vanish at p M. In this paper, we will construct smooth counterexamples to the Weyl Vanishing Conjecture for any n ≥ 25.

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U2 - 10.1007/s00526-009-0233-6

DO - 10.1007/s00526-009-0233-6

M3 - Article

AN - SCOPUS:70350749387

SN - 0944-2669

VL - 36

SP - 377

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 3

ER -

Blow-up examples for the Yamabe problem

Abstract

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