3 problems
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Conjecture that higher-dimensional Harnack geometry is governed by circular arcs
Circular-arc conjecture. In higher dimensions, a similar connection with circular geometry should persist, and the curve sought for the Harnack inequality should be an arc of a cir…
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Conjecture on verifying assumption (A4) for more general subordinators
Let be the function associated with the subordinator in the paper, and suppose that assumption (A4) requires that, for every , there exist a function and…
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Finite-time blow-up for critical data with compactly supported kernels
Let be a convolution kernel, and consider the nonlocal heat equation with initial data whose growth is critical at the rate . For gaussian kernels, Theorem 2 states…