论文标题
带有光纤边界I的流形的热型方程I：Schauder估计值
Heat-type equations on manifolds with fibered boundary I: Schauder estimates
论文作者
论文摘要
在本文中，我们证明了带有光纤边界的歧管$ M $上的Laplace-Beltrami操作员的抛物线schauder估计，$φ$ - metric $g_φ$。这种设置概括了渐近的圆锥形（散射）空间，并包括特殊的磁性和引力单孔的情况。本文结合第二部分，为即将在这种情况下进行几何流动的讨论奠定了关键的基础。尤其是yamabe和平均曲率流。
In this paper we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold $M$ with fibered boundary and a $Φ$-metric $g_Φ$. This setting generalizes the asymptotically conical (scattering) spaces and includes special cases of magnetic and gravitational monopoles. This paper, combined with part II, lay the crucial groundwork for forthcoming discussions on geometric flows in this setting; especially the Yamabe- and mean curvature flow.
