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TTT T T T TTTTTT T T T T T Geometry & Topology msp Volume 26 (2022) Ancient mean …

We study translating solitons for the mean curvature flow, $\Sigma^ 2\subseteq\mathbb {R}^
3$ which are contained in slabs, and are of finite genus and finite entropy. As a first …

We prove a rigidity result for mean curvature self-translating solitons, characterizing the grim
reaper cylinder as the only finite entropy self-translating 2-surface in $\mathbb {R}^ 3$ of …

We classify all the translating solitons to the mean curvature flow in the three-dimensional
Heisenberg group that are invariant under the action of some one-parameter group of …

We study properly immersed ancient solutions of the codimension one mean curvature flow
in $ n $-dimensional Euclidean space, and classify the convex hulls of the subsets of space …

We construct closed, embedded, ancient mean curvature flows in each dimension with the
topology of. These examples are not mean convex and not solitons. They are constructed by …

In this work we show that 2-dimensional, simply connected, translating solitons of the mean
curvature flow embedded in a slab of ℝ3 with entropy strictly less than 3 must be mean …

We show that a complete translating soliton in Euclidean space with either finite entropy or
Euclidean volume growth is proper. For any translating soliton, whether it is proper or not …

In this paper, we explore certain properties of λ-translators, which can be regarded as a
natural generalization of translators. We first obtain a rigidity result for a complete λ …

By introducing a more flexible notion of convexity, we obtain a new Omori-Yau maximum
principle for harmonic maps. In the spirit of the Calabi-Yau conjectures, this principle is more …