A gluing approach for the fractional Yamabe problem with isolated singularities
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W. Ao, H. Chan, A. DelaTorre, M. Fontelos, M. González and J. Wei, On higher-dimensional singularities for the fractional Yamabe problem: A non-local Mazzeo–Pacard program, preprint (2018), https://arxiv.org/abs/1802.07973.
W. Ao, H. Chan, M. González and J. Wei, Existence of positive weak solutions with a prescribed singular set of fractional Lane–Emden equations, Calc. Var. Partial Differential Equations 57 (2018), no. 6, Paper No. 149.
W. Ao, M. González and Y. Sire, Boundary connected sum of Escobar manifolds, preprint (2018), https://arxiv.org/abs/1807.06691.
W. Ao, M. Musso and J. Wei, On spikes concentrating on line-segments to a semilinear Neumann problem, J. Differential Equations 251 (2011), no. 4–5, 881–901.
A. Bahri, Critical points at infinity in some variational problems, Pitman Res. Notes Math. Ser. 182, Longman Scientific, Harlow 1989.
L. Caffarelli, T. Jin, Y. Sire and J. Xiong, Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities, Arch. Ration. Mech. Anal. 213 (2014), no. 1, 245–268.
L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), no. 7–9, 1245–1260.
J. S. Case and S.-Y. A. Chang, On fractional GJMS operators, Comm. Pure Appl. Math. 69 (2016), no. 6, 1017–1061.
S.-Y. A. Chang and M. d. M. González, Fractional Laplacian in conformal geometry, Adv. Math. 226 (2011), no. 2, 1410–1432.
J. Dávila, M. del Pino and Y. Sire, Nondegeneracy of the bubble in the critical case for nonlocal equations, Proc. Amer. Math. Soc. 141 (2013), no. 11, 3865–3870.
A. DelaTorre, M. del Pino, M. d. M. González and J. Wei, Delaunay-type singular solutions for the fractional Yamabe problem, Math. Ann. 369 (2017), no. 1–2, 597–626.
A. DelaTorre and M. González, Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry, preprint (2015), https://arxiv.org/abs/1504.03493; to appear in Rev. Mat. Iberoam.
C. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante, J. Math. Pures Appl. 6 (1841), 309–314.
E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math. 136 (2012), no. 5, 521–573.
Y. Fang and M. d. M. González, Asymptotic behavior of Palais–Smale sequences associated with fractional Yamabe-type equations, Pacific J. Math. 278 (2015), no. 2, 369–405.
M. d. M. González, R. Mazzeo and Y. Sire, Singular solutions of fractional order conformal Laplacians, J. Geom. Anal. 22 (2012), no. 3, 845–863.
M. d. M. González and J. Qing, Fractional conformal Laplacians and fractional Yamabe problems, Anal. PDE 6 (2013), no. 7, 1535–1576.
M. d. M. González and M. Wang, Further results on the fractional Yamabe problem: The umbilic case, J. Geom. Anal. 28 (2018), no. 1, 22–60.
T. Jin, O. S. de Queiroz, Y. Sire and J. Xiong, On local behavior of singular positive solutions to nonlocal elliptic equations, Calc. Var. Partial Differential Equations 56 (2017), no. 1, Article ID 9.
N. Kapouleas, Complete constant mean curvature surfaces in Euclidean three-space, Ann. of Math. (2) 131 (1990), no. 2, 239–330.
S. Kim, M. Musso and J. Wei, A non-compactness result on the fractional Yamabe problem in large dimensions, J. Funct. Anal. 273 (2017), no. 12, 3759–3830.
S. Kim, M. Musso and J. Wei, Existence theorems of the fractional Yamabe problem, Anal. PDE 11 (2018), no. 1, 75–113.
A. Malchiodi, Some new entire solutions of semilinear elliptic equations on ℝn{\mathbb{R}^{n}}, Adv. Math. 221 (2009), no. 6, 1843–1909.
R. Mazzeo, Elliptic theory of differential edge operators. I, Comm. Partial Differential Equations 16 (1991), no. 10, 1615–1664.
R. Mazzeo and F. Pacard, Constant scalar curvature metrics with isolated singularities, Duke Math. J. 99 (1999), no. 3, 353–418.
R. Mazzeo and F. Pacard, Constant mean curvature surfaces with Delaunay ends, Comm. Anal. Geom. 9 (2001), no. 1, 169–237.
R. Mazzeo, F. Pacard and D. Pollack, Connected sums of constant mean curvature surfaces in Euclidean 3 space, J. reine angew. Math. 536 (2001), 115–165.
R. Mazzeo, D. Pollack and K. Uhlenbeck, Connected sum constructions for constant scalar curvature metrics, Topol. Methods Nonlinear Anal. 6 (1995), no. 2, 207–233.
R. Mazzeo and B. Vertman, Elliptic theory of differential edge operators, II: Boundary value problems, Indiana Univ. Math. J. 63 (2014), no. 6, 1911–1955.
R. M. Schoen, The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Comm. Pure Appl. Math. 41 (1988), no. 3, 317–392.
R. M. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Topics in calculus of variations (Montecatini Terme 1987), Lecture Notes in Math. 1365, Springer, Berlin (1989), 120–154.