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See detailHeat equation in vector bundles with time-dependent metric
Philipowski, Robert UL; Thalmaier, Anton UL

in Journal of the Mathematical Society of Japan [=JMSJ] (2015), 67(4), 1759-1769

We derive a stochastic representation formula for solutions of heat-type equations on vector bundles with time-dependent Riemannian metric over manifolds whose Riemannian metric is time-dependent as well ... [more ▼]

We derive a stochastic representation formula for solutions of heat-type equations on vector bundles with time-dependent Riemannian metric over manifolds whose Riemannian metric is time-dependent as well. As a corollary we obtain a vanishing theorem for bounded ancient solutions under a curvature condition. Our results apply in particular to the case of differential forms. [less ▲]

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See detailA smooth family of intertwining operators
Lahiani, Raza UL; Molitor-Braun, Carine UL

in Journal of the Mathematical Society of Japan [=JMSJ] (2011), 63(1), 321-361

Detailed reference viewed: 53 (4 UL)