MathDBHeat kernel estimate implies energy comparability
Heat kernel estimate implies energy comparability
Let (KE) denote the energy-comparability property, and suppose a metric measure space admits a heat kernel satisfying the heat kernel estimate (hk). Heat-kernel implication question. Does the heat kernel estimate (hk) imply (KE)? The source lists this as an open problem concerning whether heat-kernel estimates force energy comparability for general ; no resolution is given.
Sources & referencesView supporting material
Primary source
Jin Gao, Zhenyu Yu and Junda Zhang, “Heat kernel-based p-energy norms on metric measure spaces”, arXiv:2303.10414 (2026).
Additional references
5 papers in this index state this conjecture (2004–2023). The statement above is taken from the most recent of them; the others are arXiv:2205.06100, arXiv:1606.08601, arXiv:1209.0665, arXiv:math/0409308.
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