Existence of conformal metrics with constant Q-curvature

By Z. Djadli, A. Malchiodi. 2004

285 citations recorded by the source corpus.

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the compactness result of [35].

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/d49300574b55d763912b41fadfbea532be5aa382

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In Applied Mathematics

Citations in the corpus

An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, methodology): “As we will try to describe, our approach combines the scaling invariance properties in [53] and the possibility of volume concentration at multiple points (as in [34], [35]).”
The Paneitz equation in hyperbolic space (2008, background): “Recent work of Djadli and Malchiodi [ 13 ] provides further extensions and completions of these works.”
Constant Q-curvature metrics in arbitrary dimension (2007, methodology): “Hence we will use a min-max scheme following the method of Djadli and Malchiodi in [ 26 ].”
Q‐Curvature on a Class of Manifolds with Dimension at Least 5 (2014, background): “The dimension 4 case does not suffer from this difficulty and was treated in many articles such as [4, 7, 10].”
Kazdan–Warner equation on graph (2016, background): “pper solution. Consequently, c−(h) = −∞ if h ≤ 0 but h .0. 7. Some extensions The equation (2) involving higher order diﬀerential operators was also extensively studied on manifolds, see for examples [6, 7] and the references therein. In this section, we shall extend Theorems 1-4 to nonlinear ellipt”
Some existence results for the Toda system on closed surfaces (2007, methodology): “Proof of Proposition 3.1. We modify the argument in [11] and [ 15 ].”
Blow-up analysis of a Finsler–Liouville equation in two dimensions☆ (2012, methodology): “A general existence result might be obtained by using an argument of Djadli and Malchiodi [20].”
Weighted barycentric sets and singular Liouville equations on compact surfaces (2011, methodology): “Moreover, we can exploit a well-known result asserting that if Σ is a compact surface with no boundary, then Σk is not contractible for any k ≥ 1 (see [23] for a sketch of the argument given in [2]): once we prove that Σk is homotopy equivalent to J−L ρ = { u ∈ H (Σ, g) |Jρ(u) ≤ −L } (for L 1), we g”
Supercritical conformal metrics on surfaces with conical singularities (2011, background): “2 and by arguing as in [24] we obtain the following result.”
The Nirenberg problem and its generalizations: a unified approach (2014, background): “[48], Qing and Raske [68], Djadli and Malchiodi [25], Ndiaye [66], Weinstein and Zhang [74], Hebey and Robert [47], Li et al.”