No abstract

In this article, we prove a general and rather flexible upper bound for the heat kernel of a weighted heat operator on a closed manifold evolving by an intrinsic geometric flow. The proof is based on logarithmic Sobolev inequalities and ultracontractivity estimates for the weighted operator along the flow, a method which was previously used by Davies [11] in the case of a non-evolving manifold. This result directly implies Gaussian-type upper bounds for the heat kernel under certain bounds on the evolving distance function; in particular we find new proofs of Gaussian heat kernel bounds on manifolds evolving by Ricci flow with bounded curvature or positive Ricci curvature. We also obtain similar heat kernel bounds for a class of other geometric flows. − d 2 g(t) (x,y) C(t−s) , for any x, y ∈ M and 0 ≤ s < t ≤ T .

We prove bubble-tree convergence of sequences of gradient Ricci shrinkers with uniformly bounded entropy and uniform local energy bounds, refining the compactness theory of Haslhofer and Müller (Geom Funct Anal 21:1091–1116, 2011; Proc Am Math Soc 143(10):4433–4437, 2015). In particular, we show that no energy concentrates in neck regions, a result which implies a local energy identity for the sequence. Direct consequences of these results are an identity for the Euler characteristic and a local diffeomorphism finiteness theorem.

Past research has explored how travelers make economic decisions, but only a small number of papers look at financial nudges and price anchoring—how they might cause travelers to make snap judgements about value that undermine rational economic principles. This research explores the behavioral response to different kinds of incentives. It finds that, consistent with theory, when presented with two numbers certain individuals will anchor to a higher number and be willing to pay more. Likewise, it finds that certain consumers are not able to quickly make judgements about the cost of travel. When the survey participants were offered daily or monthly payment plans, payments each day were valued almost twice as much as a single payment each month. This offers important policy considerations for public agencies seeking to reduce driving, particularly as new disruptive platforms emerge and new technology allows for more dynamic and curated data to be used to nudge travel behavior.