Isoperimetric constants and estimates of heat kernels of pre Sierpinski carpets (Q1826223)

The author calculated isoperimetric constants of the n-dimensional pre Sierpinski carpet \({\mathcal I}_ n\). As an application, he obtained the following estimate of the Neumann heat kernel \(p_ n(t,x,y)\) on \({\mathcal I}_ n:\) \[ p_ n(t,x,y)\leq const.t^{-d(n)/2}\quad for\quad 1\leq t<\infty,\quad x,y\in {\mathcal I}_ n, \] where \(d(n)=\log (3^ n- 1)/\{\log (3^ n-1)-\log (3^{n-1}-1)\}\).