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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

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Gaussian heat kernel bounds on Riemannian manifolds [duplicate]

I wish to know if we have Gaussian lower and upper bounds for the heat kernel,i.e. $$ t^{-n/2}e^{-\frac{\rho(x,y)^2}{C_1t}} \lesssim p_t(x,y) \lesssim t^{-n/2}e^{-\frac{\rho(x,y)^2}{C_2t}}, $$ on a c …
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