On Singular Yamabe Obstructions
The Journal of Geometric Analysis(2022)
摘要
We discuss the obstruction to the existence of a smooth solution of a singular version of the Yamabe problem for a hypersurface in a four-dimensional general background. This obstruction is a conformally invariant density. We derive various explicit formulas for the singular Yamabe obstruction directly from the original definition. We discuss in detail the relation to results in the literature.
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关键词
Conformal geometry, Hypersurface invariant, Poincaré–Einstein metric, Singular Yamabe problem, Yamabe obstruction, Willmore functional, Primary 53B20, 53B25, 53C18, Secondary 53C25
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