Conformal metrics of constant scalar curvature with unbounded volumes

Key Points

Key points are not available for this paper at this time.

Abstract

For n 25, we construct a smooth metric g on the standard n-dimensional sphere Sⁿ such that there exists a sequence of smooth metrics \gₖ\₊ conformal to g where each gₖ has scalar curvature R₆䂵 1 and their volumes Vol (Sⁿ, gₖ) tend to infinity as k approaches infinity.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper

Cite This Study

Gong et al. (Mon,) studied this question.

synapsesocial.com/papers/68e6577ab6db6435875e6bd1 https://doi.org/https://doi.org/10.48550/arxiv.2406.06898

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1On the Scalar Curvature Compactness Conjecture in the Conformal Case2024
2Nonhomothetic complete periodic metrics with constant scalar curvature2025
3Constant scalar curvature metrics with isolated singularities1999 · 136 citations
4Smoothing $$L^\infty $$ Riemannian metrics with nonnegative scalar curvature outside of a singular set2026
5A gluing construction of singular solutions for a fully non-linear equation in conformal geometry2024

Mark Helpful

Bookmark

Relay

View Full Paper