论文标题
锚定的热内核上限在具有无界几何形状和防树的图形上
Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees
论文作者
论文摘要
我们在图形上的固定原点在大时段的固定原点上得出了高斯的热内核边界，在大球上的索波列夫不等式和体积增加一倍的情况下。我们以前的工作[KR22]的上限受到测量到原点距离的新校正项的影响。然后将主要结果应用于具有无界顶点程度的抗树，首次为此类图产生高斯上限。为了证明这一点，我们表明有关固有指标的等量估计会产生Sobolev的不平等。最后，我们证明了抗树是常规的，并且它们满足了更大维度的等值不平等。
We derive Gaussian heat kernel bounds on graphs with respect to a fixed origin for large times under the assumption of a Sobolev inequality and volume doubling on large balls. The upper bound from our previous work [KR22] is affected by a new correction term measuring the distance to the origin. The main result is then applied to anti-trees with unbounded vertex degree, yielding Gaussian upper bounds for this class of graphs for the first time. In order to prove this, we show that isoperimetric estimates with respect to intrinsic metrics yield Sobolev inequalities. Finally, we prove that anti-trees are Ahlfors regular and that they satisfy an isoperimetric inequality of a larger dimension.
