论文标题
Laplacian在分析性超表面上的小时热量膨胀，具有孤立的奇异性
Small time heat expansion of the laplacian on an analytic hypersurface with an isolated singularity
论文作者
论文摘要
我证明了在具有孤立奇异性的分析性超表面上，拉普拉斯算子的小时热膨胀存在。首先，我们获得了奇异性附近的高表情的局部参数化。我们介绍了准切线锥的概念。然后使用牛顿方案驱动锥体的参数化，并获得具有特定形式函数的参数化。这些使我们能够在奇异性附近获得拉普拉斯操作员的本地模型。这些是具有不规则奇异性的操作员。我们得出单数渐近学所需的估计值。
I prove the existence of small time heat expansion for the Laplace operator on an analytic hypersurface with an isolated singularity. First we obtain a local parametrization of the hypersurface near the singularity. We introduce the notion of quasihomogeneous tangent cone. Then perturb the parametrization of the cone employing a Newton scheme and obtain a parametrization with functions of specific form. These allow us to obtain local models for the Laplace operator near the singularity. These are operators with irregular singularities. We derive the estimates required by singular asymptotics.
