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Open AccessOn the \(H^1(ds^\gamma )\) -Gradient Flow for the Length Functional
In this article, we consider the length functional defined on the space of immersed planar curves. The \(L^2(ds^\gamma )\) ...
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On an inverse curvature flow in two-dimensional space forms
We study the evolution of compact convex curves in two-dimensional space forms. The normal speed is given by the difference of the weighted inverse curvature with the support function, and in the case where th...
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A gradient flow for the p-elastic energy defined on closed planar curves
We study the evolution of closed inextensible planar curves under a second order flow that decreases the p-elastic energy. A short time existence result for \(p \in (1, \infty ) \) p ∈ ( 1 , ∞ ) is obtained...
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Open AccessPublisher Correction: Genetic tool development in marine protists: emerging model organisms for experimental cell biology
An amendment to this paper has been published and can be accessed via a link at the top of the paper.
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Open AccessGenetic tool development in marine protists: emerging model organisms for experimental cell biology
Diverse microbial ecosystems underpin life in the sea. Among these microbes are many unicellular eukaryotes that span the diversity of the eukaryotic tree of life. However, genetic tractability has been limite...
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A rigidity theorem for ideal surfaces with flat boundary
We consider surfaces with boundary satisfying a sixth-order nonlinear elliptic partial differential equation corresponding to extremising the \(L^2\)L2-norm of the gradient of the mean curvature. We show that suc...
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A Rigidity Theorem for Ideal Surfaces with Flat Boundary
We are interested in surfaces with boundary satisfying a sixth order non-linear elliptic partial differential equation associated with extremal surfaces of the L2-norm of the gradient of the mean curvature. We sh...
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The anisotropic polyharmonic curve flow for closed plane curves
We study the curve diffusion flow for closed curves immersed in the Minkowski plane \({\mathcal {M}}\) ...
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Chapter
A Sixth Order Curvature Flow of Plane Curves with Boundary Conditions
We show that small energy curves under a particular sixth order curvature flow with generalised Neumann boundary conditions between parallel lines converge exponentially in the C ∞ topology in infinite time to st...
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The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow
In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This reduces to studying the curve diffusion flow for the profile curve of the ribbon. We pr...
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The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow
In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This reduces to studying the curve diffusion flow for the profile curve of the ribbon. We pr...
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A classification theorem for Helfrich surfaces
In this paper we study the functional \(\mathcal W{} _{\lambda _1,\lambda _2}\) ...
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Unstable Willmore surfaces of revolution subject to natural boundary conditions
In the class of surfaces with fixed boundary, critical points of the Willmore functional are naturally found to be those solutions of the Euler-Lagrange equation where the mean curvature on the boundary vanish...
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On the curve diffusion flow of closed plane curves
In this paper, we consider the steepest descent H −1-gradient flow of the length functional for immersed plane curves, known as the curve diffusion flow. It is known that under this flow t...
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Open AccessPan genome of the phytoplankton Emiliania underpins its global distribution
A reference genome from the coccolithophore Emiliania huxleyi is presented, along with sequences from 13 additional isolates, revealing a pan genome comprising core genes and genes variably distributed between st...
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Surface diffusion flow near spheres
We consider closed immersed hypersurfaces evolving by surface diffusion flow, and perform an analysis based on local and global integral estimates. First we show that a properly immersed stationary (ΔH ≡ 0) hyper...
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Lifespan theorem for constrained surface diffusion flows
We consider closed immersed hypersurfaces in \({\mathbb R^{3}}\) and
