scholarly journals A non-compactness result on the fractional Yamabe problem in large dimensions

2017 ◽  
Vol 273 (12) ◽  
pp. 3759-3830 ◽  
Author(s):  
Seunghyeok Kim ◽  
Monica Musso ◽  
Juncheng Wei
Keyword(s):  
Yamabe Problem ◽  
Compactness Result

scholarly journals Nodal solutions for the fractional Yamabe problem on Heisenberg groups

2019 ◽  
Vol 150 (2) ◽  
pp. 771-788 ◽  
Author(s):  
Alexandru Kristály
Keyword(s):  
Weak Solutions ◽  
Unitary Group ◽  
Original Problem ◽  
Laplacian Operator ◽  
Yamabe Problem ◽  
Heisenberg Groups ◽  
Nodal Solutions ◽  
Compactness Result ◽  
Homogeneous Dimension ◽  
Nodal Properties

AbstractWe prove that the fractional Yamabe equation ${\rm {\cal L}}_\gamma u = \vert u \vert ^{((4\gamma )/(Q-2\gamma ))}u$ on the Heisenberg group ℍn has [n + 1/2] sequences of nodal (sign-changing) weak solutions whose elements have mutually different nodal properties, where ${\rm {\cal L}}_\gamma $ denotes the CR fractional sub-Laplacian operator on ℍn, Q = 2n + 2 is the homogeneous dimension of ℍn, and $\gamma \in \bigcup\nolimits_{k = 1}^n [k,((kQ)/Q-1)))$. Our argument is variational, based on a Ding-type conformal pulling-back transformation of the original problem into a problem on the CR sphere S2n + 1 combined with a suitable Hebey-Vaugon-type compactness result and group-theoretical constructions for special subgroups of the unitary group U(n + 1).

Linear perturbations of the fractional Yamabe problem on the minimal conformal infinity

2021 ◽  
Vol 29 (2) ◽  
pp. 363-407
Author(s):  
Shengbing Deng ◽  
Seunghyeok Kim ◽  
Angela Pistoia
Keyword(s):  
Yamabe Problem ◽  
Linear Perturbations

Variational structure of the vn2-Yamabe problem

2018 ◽  
Vol 56 ◽  
pp. 187-201 ◽  
Author(s):  
Matthew Gursky ◽  
Jeffrey Streets
Keyword(s):  
Yamabe Problem ◽  
Variational Structure

scholarly journals Solution of the Boolean Markus–Yamabe Problem

1999 ◽  
Vol 22 (1) ◽  
pp. 60-102 ◽  
Author(s):  
Mau-Hsiang Shih ◽  
Juei-Ling Ho
Keyword(s):  
Yamabe Problem
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