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Mean curvature blow up in mean curvature flow
In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds are characterised by the blow up of the mean curvature.
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Microglia (BV2) and IL‐4‐treated BMDMs promote astrocytoma clustering and inhibit tumor growth, not shown in other macrophage cells. In vivo, microglial co‐implantation enhances CD8+ T cell infiltration, elevates Granzyme B, lowers circulating MDSCs, and extends survival only in immune‐competent mice, but not in immune‐deficient mice.
Tzu‐Chieh Sun+5 more
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Some comments on gravitational entropy and the inverse mean curvature flow [PDF]
G. W. Gibbons
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A concentration phenomenon in mean curvature flow [PDF]
The mean curvature flow is the evolution of hypersurfaces by their mean curvature vectors and is described by the equation \({\partial f_ t\over \partial t} = H_{f_ t}\) where \(f_ t\) is an immersion of a compact smooth hypersurface of \(\mathbb{R}^{n+1}\) and \(H_{f_ t}\) denotes its curvature vector. The solution of this equation depends on the form
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In this exploratory study, we investigated the relationship between the gut microbiota and outcome in patients with metastatic hormone receptor‐positive breast cancer, treated in a randomized clinical trial with chemotherapy alone or chemotherapy in combination with immune checkpoint blockade.
Andreas Ullern+7 more
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Mean curvature flow on Ricci solitons [PDF]
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Cleavable N‐terminal Thioredoxin fusion enabled soluble expression and purification of otherwise insoluble SARS‐CoV‐2 Nucleocapsid (N) protein. A four‐step purification strategy yielded highly homogeneous, RNA‐free N protein. Binding assays showed high RNA affinity (Kd ~ 28 nm). The study will facilitate high‐resolution structural studies of N protein,
Shweta Singh, Gagan D. Gupta
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Drag Reduction Effects of Micro-Bubbles in Straight and Helical Pipes
Experimental investigations were conducted to study the effect of micro-bubbles injected into water flowing through straight and helical pipes with different curvature ( 0.025, 0.05 and 0.1).
Mohammed M. E. SHATAT+3 more
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Self-intersections for the surface diffusion and the volume-preserving mean curvature flow [PDF]
Uwe Mayer, Gieri Simonett
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