Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the CR Nirenberg problem: density and multiplicity of solutions (2404.13622v1)

Published 21 Apr 2024 in math.AP

Abstract: We prove some results on the density and multiplicity of positive solutions to the prescribed Webster scalar curvature problem on the $(2n+1)$-dimensional standard unit CR sphere $(\mathbb{S} {2n+1},\theta_0)$. Specifically, we construct arbitrarily many multi-bump solutions via the variational gluing method. In particular, we show the Webster scalar curvature functions of contact forms conformal to $\theta_0$ are $C{0}$-dense among bounded functions which are positive somewhere. Existence results of infinitely many positive solutions to the related equation $-\Delta_{\mathbb{H}} u=R(\xi) u{(n+2) /n}$ on the Heisenberg group $\Hn $ with $R(\xi)$ being asymptotically periodic with respect to left translation are also obtained. Our proofs make use of a refined analysis of bubbling behavior, gradient flow, Pohozaev identity, as well as blow up arguments.

Summary

We haven't generated a summary for this paper yet.