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The conjecture that the volume-doubling implication extends to spatially dependent volume functions
Volume-doubling generalisation conjecture. The condition $(\mathrm{bacra})$ should imply $(DU\!E^v)$ even when $v$ depends on $x$ .
Conjectureopendoubling-metric-measure-spaces functional-inequalities heat-kernel-estimatesarXiv posted 2 days ago

The conjecture that the volume-doubling implication extends to spatially dependent volume functions