Prescribing Morse scalar curvatures

DOI10.1007/s00032-022-00374-xOpenAlexW4312193662MaRDI QIDQ6044480

Andrea Malchiodi

Publication date: 19 May 2023

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-022-00374-x

zbMATH Keywords

variational methodsblow-up analysisgeometric PDEs

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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• The scalar curvature flow on \(S ^{n }\)-perturbation theorem revisited
• The scalar-curvature problem on the standard three-dimensional sphere
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Conformal metrics with prescribed scalar curvature
• The existence of minimal immersions of 2-spheres
• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• Scalar curvature and conformal deformation of Riemannian structure
• Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures
• Estimate of the conformal scalar curvature equation via the method of moving planes. II
• Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
• The scalar curvature equation on 2- and 3-spheres
• On a variational problem with lack of compactness: The topological effect of the critical points at infinity
• Elliptic partial differential equations of second order
• Infinite dimensional Morse theory and multiple solution problems
• On the prescribed scalar curvature problem on 4-manifolds
• Sobolev spaces on Riemannian manifolds
• Extremal metrics of zeta function determinants on 4-manifolds
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Compactness and stability for nonlinear elliptic equations
• Curvature functions for compact 2-manifolds
• Prescribing Morse scalar curvatures: subcritical blowing-up solutions
• A flow approach to Nirenberg's problem
• Perturbative techniques in conformal geometry
• Conformal scalar curvature equation on Sn: Functions with two close critical points (Twin Pseudo-Peaks)
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• The Yamabe problem
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Estimates of the conformal scalar curvature equation via the method of moving planes
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness
• Prescribing Morse Scalar Curvatures: Blow-Up Analysis
• Variational Methods
• The conjectures on conformal transformations of Riemannian manifolds