»ã±¨±êÌâ (Title)£º ´ø±ß½ôÁ÷ÐÎÉÏ$\sigma_{2}$ÇúÂÊ·½³Ì£¨The $\sigma_{2}$-curvature equation on a compact manifold with boundary£©

»ã±¨ÈË (Speaker)£º Τí| ×êÑÐÔº£¨ÄϾ©´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ2ÈÕ (ÖÜËÄ) 10:00-12:00

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»ã±¨ÌáÒª£ºWe first establish local $C^2$ estimates of solutions to the $\sigma_2$-curvature equation with nonlinear Neumann boundary condition. Then, under assumption that the background metric has nonnegative mean curvature on totally non-umbilic boundary, for dimensions three and four we prove the existence of a conformal metric with a prescribed positive $\sigma_2$-curvature function and a prescribed nonnegative boundary mean curvature function. The local estimates play an important role in blow up analysis in the latter existence result.