arXiv (OAI Expanded)
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Diffusion and reaction in the quasi-spherical equation: mean curvature deformations for fill-Ins
We study the diffusion and reaction effects of Bartnik's quasi-spherical equation to deform boundary mean curvature in fill-in problems with scalar curvature bounded below. The diffusion effect yields an explicit $L^p$-to-$L^\infty$ estimate for $\partial_tu=u^2Δu$, thereby extending the known upper
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