论文标题
RICCI的熵流具有I型标量曲率边界
The Entropy of Ricci Flows with Type-I Scalar Curvature Bounds
论文作者
论文摘要
在本文中，我们扩展了RICCI流动的理论，即在有限的奇异性下满足I型标量曲率条件。在[BAM16]中，Bamler表明，I型恢复程序将产生一个具有奇异性4的奇异梯度Ricci孤子4。我们证明，基于奇异时间的共轭热内核的熵会融合到奇异的soliton sotil from flot from from flow flow flow frow flow flow flow flow frow from inicci from from inicci from from inicci from from frove frove from from from from from from flow frove from from from from from folke from folke from noce sef。这概括了先前仅在更强烈的I型曲率结合的情况下知道的结果。我们还表明，在尺寸4中，奇异的soliton远离有限的多个点，这是圆锥光滑的圆锥形奇异性
In this paper, we extend the theory of Ricci flows satisfying a Type-I scalar curvature condition at a finite-time singularity. In [Bam16], Bamler showed that a Type-I rescaling procedure will produce a singular shrinking gradient Ricci soliton with singularities of codimension 4. We prove that the entropy of a conjugate heat kernel based at the singular time converges to the soliton entropy of the singular soliton, and use this to characterize the singular set of the Ricci flow solution in terms of a heat kernel density function. This generalizes results previously only known with the stronger assumption of a Type-I curvature bound. We also show that in dimension 4, the singular Ricci soliton is smooth away from finitely many points, which are conical smooth orbifold singularities
