Year: 2023
Type: preprint
Abstract: Given any asymptotically flat 3-manifold $(M,g)$ with smooth, non-empty, compact boundary $Σ$, the conformal conjecture states that for every $δ>0$, there exists a metric $g' = u^4 g$, with $u$ a harmonic function, such that the area of outermost minimal area enclosure $\tildeΣ_{g'}$ of $Σ$ with respect to $g'$ is less than $δ$. Recently, the conjecture was used to prove the Riemannian Penrose inequality for black holes with zero horizon area, and was proven to be true under the assumption of existence of only a finite number of minimal area enclosures of boundary $Σ$, and boundedness of harmonic function $u$. We prove the conjecture assuming only the boundedness of $u$.
Source: arXiv (Cornell University)
Author: Kumar, Sameer
Institution: Moscow Institute of Physics and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4382491444