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control theory 1geometric control 1heat equation 1metric measure spaces 1spectral analysis 1weighted observability 1

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math.AP2026

Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces

Vincent Boulard, Amaury Hayat, Emmanuel Trélat

The paper proves that the exponential small‑time factor e^{-γ/t} in weighted observability inequalities for heat equations is dictated by the geometry of the observation set, estab…