The paper considers a manifold M evolving under the Ricci flow and establishes a series of
gradient estimates for positive solutions of the heat equation on M. Among other results, we …

Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent
years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I …

We prove Gaussian type bounds for the fundamental solution of the conjugate heat equation
evolving under the Ricci flow. As a consequence, for dimension 4 and higher, we show that …

This is the first of a series of papers, where we introduce a new class of estimates for the
Ricci flow, and use them both to characterize solutions of the Ricci flow and to provide a …

We study the heat equation on time‐dependent metric measure spaces (as well as the dual
and the adjoint heat equation) and prove existence, uniqueness, and regularity. Of particular …

In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free
Harnack inequality for the heat equation $\partial_t u= Lu $ associated with the time …

We define horizontal diffusion in C 1 path space over a Riemannian manifold and prove its
existence. If the metric on the manifold is developing under the forward Ricci flow, horizontal …

We study the problem of non-explosion of diffusion processes on a manifold with time-
dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode …

This is the first of a series of papers, where we introduce a new class of estimates for the
Ricci flow, and use them both to characterize solutions of the Ricci flow and to provide a …

Propagation in quantum walks is revisited by showing that very general 1D discrete-time
quantum walks with time-and space-dependent coefficients can be described, at the …