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<p>We provide a rigorous analysis of the generalized Jang equation in the asymptotically anti-de Sitter setting modelled on constant time slices of anti-de Sitter spacetimes in dimensions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10455_2025_10013_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\le n \le 7\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mn>7</mn> </mrow> </math></EquationSource> </InlineEquation> for a very general class of asymptotics. Potential applications to spacetime positive mass theorems for asymptotically anti-de Sitter initial data sets are discussed.</p>

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On the existence and properties of solutions of the generalized Jang equation with respect to asymptotically anti-de Sitter initial data

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  • 发表日期：

    2025年8月4日

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  • Benjamin Meco

摘要

We provide a rigorous analysis of the generalized Jang equation in the asymptotically anti-de Sitter setting modelled on constant time slices of anti-de Sitter spacetimes in dimensions \(3\le n \le 7\) 3 ≤ n ≤ 7 for a very general class of asymptotics. Potential applications to spacetime positive mass theorems for asymptotically anti-de Sitter initial data sets are discussed.