The Nirenberg problem and its generalizations: a unified approach

By Tianling Jin, Yanyan Li, Jingang Xiong. 2014

82 citations recorded by the source corpus.

Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations $$P_\sigma (v)= Kv^{\frac{n+2\sigma }{n-2\sigma }}$$Pσ(v)=Kvn+2σn-2σ on the standard unit sphere $$\mathbb {S}^n$$Sn for all $$\sigma \in (0,n/2)$$σ∈(0,n/2), where $$P_\sigma $$Pσ is the intertwining operator of order $$2\sigma $$2σ. Finding positive solutions of these equations is equivalent to seeking metrics in the conformal class of the standard metric on spheres with prescribed certain curvatures. When $$\sigma =1$$σ=1, it is the prescribing scalar curvature problem or the Nirenberg problem, and when $$\sigma =2$$σ=2, it is the prescribing Q-curvature problem.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e597098512a64a5b31df62fb39da23becbff33fa

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In Applied Mathematics

1. Tianling Jin
2. Jingang Xiong
3. Yanyan Li
4. Wenxiong CHEN *

In Computational Theory and Mathematics

1. Jingang Xiong
2. Tianling Jin
3. Wenxiong CHEN *
4. Yanyan Li

Citations in the corpus

• Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities (2019, methodology): “3 in [26] that sup B1/2(x) v ≤ C inf B1/2(x) v.”