Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

Maria Medina; Monica Musso; Juncheng Wei

doi:10.1016/j.jfa.2019.02.001

Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

Maria Medina, Monica Musso, Juncheng Wei

Department of Mathematical Sciences

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

14 Citations (SciVal)

55 Downloads (Pure)

Abstract

Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula presented]|u| ^{[Formula presented]} u,u∈D ^1,2 (R ⁿ ). The case n=4 is the first example in the literature of a solution with maximal rank N=2n+1+[Formula presented].

Original language	English
Pages (from-to)	2470-2523
Number of pages	54
Journal	Journal of Functional Analysis
Volume	276
Issue number	8
Early online date	13 Feb 2019
DOIs	https://doi.org/10.1016/j.jfa.2019.02.001
Publication status	Published - 15 Apr 2019

Keywords

Entire solutions
Gluing methods
Rigidity properties for entire solutions
Yamabe problem

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2019.02.001

MaximalSolution-revised for JFA.PDFAccepted author manuscript, 264 KBLicence: CC BY-NC-ND

Cite this

@article{924a3497c69840d2be14a4320f76456d,

title = "Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank",

abstract = " Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula presented]|u| [Formula presented] u,u∈D 1,2 (R n ). The case n=4 is the first example in the literature of a solution with maximal rank N=2n+1+[Formula presented]. ",

keywords = "Entire solutions, Gluing methods, Rigidity properties for entire solutions, Yamabe problem",

author = "Maria Medina and Monica Musso and Juncheng Wei",

year = "2019",

month = apr,

day = "15",

doi = "10.1016/j.jfa.2019.02.001",

language = "English",

volume = "276",

pages = "2470--2523",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier Academic Press Inc",

number = "8",

}

TY - JOUR

T1 - Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

AU - Medina, Maria

AU - Musso, Monica

AU - Wei, Juncheng

PY - 2019/4/15

Y1 - 2019/4/15

N2 - Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula presented]|u| [Formula presented] u,u∈D 1,2 (R n ). The case n=4 is the first example in the literature of a solution with maximal rank N=2n+1+[Formula presented].

AB - Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula presented]|u| [Formula presented] u,u∈D 1,2 (R n ). The case n=4 is the first example in the literature of a solution with maximal rank N=2n+1+[Formula presented].

KW - Entire solutions

KW - Gluing methods

KW - Rigidity properties for entire solutions

KW - Yamabe problem

UR - http://www.scopus.com/inward/record.url?scp=85061618944&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2019.02.001

DO - 10.1016/j.jfa.2019.02.001

M3 - Article

AN - SCOPUS:85061618944

SN - 0022-1236

VL - 276

SP - 2470

EP - 2523

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Concentration phenomena in nonlinear analysis

Cite this

Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Concentration phenomena in nonlinear analysis

Cite this