3 problems

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Polarizable Carnot groups are of H-type
Polarizability conjecture. Every polarizable Carnot group is of H-type; equivalently, there are no polarizable Carnot groups that are not of H-type.
Conjectureopencarnot-groups h-type-groups subelliptic-analysisarXiv posted 2 days ago
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Small-time off-diagonal boundedness conjecture for the complexified heat kernel on $\mathbf{SU}(2)$
Small-time off-diagonal boundedness conjecture. The ratio remains bounded as $t\to0$ when $R$ is sufficiently large. This conjecture concerns the short-time behavior of the complex…
Conjectureopenheat-kernels small-time-asymptotics subelliptic-analysisarXiv posted 2 days ago
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The endpoint $L^1$ gradient bound for the subelliptic heat semigroup on $\mathbf{SU}(2)$
Endpoint $L^1$ gradient-bound conjecture. The same inequality should hold for $p=1$ , namely, there should exist a constant $C_1>1$ such that for every smooth…
Conjectureopengradient-estimates heat-kernel-estimates subelliptic-analysisarXiv posted 2 days ago

Polarizable Carnot groups are of H-type