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In this work, we consider sequences of $$C^2$$ C 2 metrics which converges to a $$C^2$$ C 2 metric in $$C^0$$ C 0 sense. We show that if the scalar curvature of the sequence is almost non-negative in the integral sense, then the limiting metric has scalar curvature lower bound in point-wise sense.

In this article, we study the higher-order regularity of the Kahler-Ricci flow on compact Kahler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates on cylinders, we proved that when the generic fibers of the Iitaka fibration are biholomorphic to each other, the flow converges in C-loc(infinity)-topology away from singular fibers to a negative Kahler-Einstein metric on the base manifold. In particular, we proved that the Ricci curvature of the flow is uniformly bounded on any compact subsets away from singular fibers when the generic fibers are biholomorphic to each other. (C) 2021 Elsevier Inc. All rights reserved.

In this article, we study the higher-order regularity of the Kahler-Ricci flow on compact Kahler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates on cylinders, we proved that when the generic fibers of the Iitaka fibration are biholomorphic to each other, the flow converges in C-loc(infinity)-topology away from singular fibers to a negative Kahler-Einstein metric on the base manifold. In particular, we proved that the Ricci curvature of the flow is uniformly bounded on any compact subsets away from singular fibers when the generic fibers are biholomorphic to each other. (C) 2021 Elsevier Inc. All rights reserved.

In this article, we study the higher-order regularity of the Kahler-Ricci flow on compact Kahler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates on cylinders, we proved that when the generic fibers of the Iitaka fibration are biholomorphic to each other, the flow converges in C-loc(infinity)-topology away from singular fibers to a negative Kahler-Einstein metric on the base manifold. In particular, we proved that the Ricci curvature of the flow is uniformly bounded on any compact subsets away from singular fibers when the generic fibers are biholomorphic to each other. (C) 2021 Elsevier Inc. All rights reserved.

In this paper, we discuss uniqueness and backward uniqueness for mean curvature flow of non-compact manifolds. We use an energy argument to prove two uniqueness theorems for mean curvature flow with possibly unbounded curvatures. These generalize the results in [5]. Using similar method, we also obtain a uniqueness result on Ricci flows. A backward uniqueness theorem is also proved for mean curvature flow with bounded curvatures.

In this paper, we discuss uniqueness and backward uniqueness for mean curvature flow of non-compact manifolds. We use an energy argument to prove two uniqueness theorems for mean curvature flow with possibly unbounded curvatures. These generalize the results in [5]. Using similar method, we also obtain a uniqueness result on Ricci flows. A backward uniqueness theorem is also proved for mean curvature flow with bounded curvatures.

The cold shock domain is one of the most highly conserved motifs between bacteria and higher eukaryotes. Y-box-binding proteins represent a subfamily of cold shock domain proteins with pleiotropic functions, ranging from transcription in the nucleus to translation in the cytoplasm. These proteins have been investigated in all major model organisms except Caenorhabditis elegans. In this study, we set out to fill this gap and present a functional characterization of CEYs, the C. elegans Y-box-binding proteins. We find that, similar to other organisms, CEYs are essential for proper gametogenesis. However, we also report a novel function of these proteins in the formation of large polysomes in the soma. In the absence of the somatic CEYs, polysomes are dramatically reduced with a simultaneous increase in monosomes and disomes, which, unexpectedly, has no obvious impact on animal biology. Because transcripts that are enriched in polysomes in wild-type animals tend to be less abundant in the absence of CEYs, our findings suggest that large polysomes might depend on transcript stabilization mediated by CEY proteins

The cold shock domain is one of the most highly conserved motifs between bacteria and higher eukaryotes. Y-box-binding proteins represent a subfamily of cold shock domain proteins with pleiotropic functions, ranging from transcription in the nucleus to translation in the cytoplasm. These proteins have been investigated in all major model organisms except Caenorhabditis elegans. In this study, we set out to fill this gap and present a functional characterization of CEYs, the C. elegans Y-box-binding proteins. We find that, similar to other organisms, CEYs are essential for proper gametogenesis. However, we also report a novel function of these proteins in the formation of large polysomes in the soma. In the absence of the somatic CEYs, polysomes are dramatically reduced with a simultaneous increase in monosomes and disomes, which, unexpectedly, has no obvious impact on animal biology. Because transcripts that are enriched in polysomes in wild-type animals tend to be less abundant in the absence of CEYs, our findings suggest that large polysomes might depend on transcript stabilization mediated by CEY proteins