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We prove genuinely sharp estimates for the Jacobi heat kernels introduced inthe context of the multidimensional cone $\mathbb{V}^{d+1}$ and its surface$\mathbb{V}^{d+1}_0$. To do so, we combine the theory of Jacobi polynomials onthe cone explored by Xu with the recent techniques by Nowak, Sj\"ogren, andSzarek, developed to find genuinely sharp estimates for the spherical heatkernel.

Sharp estimates for Jacobi heat kernels in conic domains