Results 81 to 90 of about 577,330 (363)

The extension and convergence of mean curvature flow in higher codimension [PDF]

, 2011
In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension $d\geq1$, which generalizes the extension theorem for the mean curvature flow of ...
Liu, Kefeng, Xu, Hongwei, Ye, Fei, Zhao, Entao   +3 more
core  

Mean curvature flow of monotone Lagrangian submanifolds

, 2006
We use holomorphic disks to describe the formation of singularities in the mean curvature flow of monotone Lagrangian submanifolds in $\mathbb C^{n}$.Comment: 37 pages, 3 ...
G. Huisken, J.-M. Morvan, K. Groh, K. Smoczyk, K. Smoczyk, K. Smoczyk, K. Smoczyk, K. Smoczyk, K. Zehmisch, M. Gromov, M. Schwarz, Y. Chekanov, Y. Eliashberg, Y.-G. Oh   +13 more
core   +2 more sources

Gauss Maps of the Mean Curvature Flow [PDF]

Mathematical Research Letters, 2003
final version, to appear in Mathematical Research ...
openaire   +2 more sources

Characterizing the salivary RNA landscape to identify potential diagnostic, prognostic, and follow‐up biomarkers for breast cancer

Molecular Oncology, EarlyView.
This study explores salivary RNA for breast cancer (BC) diagnosis, prognosis, and follow‐up. High‐throughput RNA sequencing identified distinct salivary RNA signatures, including novel transcripts, that differentiate BC from healthy controls, characterize histological and molecular subtypes, and indicate lymph node involvement.
Nicholas Rajan, Irina Primac, Emre Etlioglu, Laurens Debruyne, Ann Janssen, Magy Sallam, Kevin Tabury, Roel Quintens, Wiebren Tjalma, Mohammed Abderrafi Benotmane   +9 more
wiley   +1 more source

Additive operator splitting scheme for a general mean curvature flow and application in edges enhancement

Journal of Numerical Analysis and Approximation Theory
Many models that use non-linear partial differential equations (PDEs) have been extensively applied for different tasks in image processing. Among these PDE-based approaches, the mean curvature flow filtering has impressive results, for which feature ...
Rafaa Chouder, Noureddine Benhamidouche
doaj   +1 more source

Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow

Open Mathematics, 2020
In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF).
Qi Xuesen, Liu Ximin
doaj   +1 more source

A local regularity theorem for mean curvature flow with triple edges

, 2017
Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow.
Schulze, Felix, White, Brian
core   +1 more source

The thresholding scheme for mean curvature flow and de Giorgi's ideas for minimizing movements [PDF]

, 2019
We consider the thresholding scheme and explore its connection to De Giorgi's ideas on gradient flows in metric spaces; here applied to mean curvature flow as the steepest descent of the interfacial area.
Tim Laux, F. Otto
semanticscholar   +1 more source

Gut microbiota diversity is prognostic in metastatic hormone receptor‐positive breast cancer patients receiving chemotherapy and immunotherapy

Molecular Oncology, EarlyView.
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, Kristian Holm, Nikolai Kragøe Andresen, Andreas Hagen Røssevold, Corinna Bang, Bjørn Naume, Johannes R. Hov, Jon Amund Kyte   +7 more
wiley   +1 more source

α-Mean curvature flow of non-compact complete convex hypersurfaces and the evolution of level sets

Advances in Nonlinear Analysis
We consider the α\alpha -mean curvature flow for convex graphs in Euclidean space. Given a smooth, complete, strictly convex, non-compact initial hypersurface over a strictly convex projected domain, we derive uniform curvature bounds, which are ...
Kang Hyunsuk, Lee Ki-Ahm, Lee Taehun
doaj   +1 more source