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pabryan / rough_metrics_heat_kernel_regularity

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Dependence of $\alpha$ on Ricci bounds #5

Open pabryan opened 6 years ago

pabryan commented 6 years ago

A few paragraphs after Thm 5.1 we assert that Ricci bounds give uniform (in $\alpha$) $C^{0,\alpha}$ bounds for the heat kernel. Check (probably in Saloff-Coste for the rough case and Li-Yau for the smooth case) that this is true.

lashputin commented 6 years ago

Remember, the $\alpha$ comes from having a nearby smooth metric, nearby in this L^\infty sense. I would expect it to depend, but I'm not sure.