Related papers: Minimal Bubbling for Willmore Surfaces

A Euclidean minimal torus with planar ends gives rise to an immersed Willmore torus in the conformal 3--sphere $S^3=\R^3\cup \{\infty\}$. The class of Willmore tori obtained this way is given a spectral theoretic characterization as the…

The notion of strictly outward minimising hull is investigated for open sets of finite perimeter sitting inside a complete noncompact Riemannian manifold. Under natural geometric assumptions on the ambient manifold, the strictly outward…

It is well-known that the Willmore flow of closed spherical immersions exists globally in time and converges if the initial datum has Willmore energy below $8\pi$ - exactly the Li-Yau energy threshold below which all closed immersions are…

We study the compactness of Willmore surfaces without assuming the convergence of the induced complex structures. In particular, we compute the energy loss in the neck in terms of the residue and we prove that the limit of the image of the…

Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking however, making actual design quite uphazard. We offer here a theory of drag reduction by…

We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent M\"obius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we…

Hypothesis: Some ions can prevent bubbles from coalescing in water. The Gibbs-Marangoni pressure has been proposed as an explanation of this phenomenon. This repulsive pressure occurs during thin film drainage whenever surface enhanced or…

For an immersed minimal surface in $\mathbb{R}^3$, we show that there exists a lower bound on its Morse index that depends on the genus and number of ends, counting multiplicity. This improves, in several ways, an estimate we previously…

In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in $\mathbb{R}^n$ with bounded total curvature. We show that (branched) conformal immersions which are close in energy to either a round…

In this paper we investigate surfaces in $\mathbb C P^2$ without complex points and characterize the minimal surfaces without complex points and the minimal Lagrangian surfaces by Ruh-Vilms type theorems. We also discuss the liftability of…

In this paper, we disprove a conjecture recently proposed in [L. Almodovar et al., arXiv:2108.00035] on the non-existence of biminimal pots realizing the cube, namely pots with the minimum number of tiles and the minimum number of bond-edge…

This paper is concerned with diffuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards…

We make some remarks about bubbling on, not necessarily proper, champs de Deligne-Mumford, i.e. compactification of the space of mappings from a given (wholly scheme like) curve, so, in particular, on quasi-projective projective varieties.…

We study the problem of existence of F-structures on compact complex surfaces, giving a complete classification modulo the gap in the classification of surfaces of class VII. We then use these results to study the minimal entropy problem…

In this paper, we show that the permeability of a porous {material} and that of a bubbly fluid are limiting cases of the complexified version of the two-fluid models posed in {Lipton_Avellaneda_1990}. We assume the viscosity of the…

In this paper we study the steepest descent $L^2$-gradient flow of the functional $\SW_{\lambda_1,\lambda_2}$, which is the the sum of the Willmore energy, $\lambda_1$-weighted surface area, and $\lambda_2$-weighted enclosed volume, for…

Motivated by applications to cell biology, we study the constrained minimization of the Helfrich energy among closed surfaces confined to a container. We show existence of minimizers in the class of bubble trees of spherical weak branched…

The well-posedness of a phase-field approximation to the Willmore flow with volume constraint is established. The existence proof relies on the underlying gradient flow structure of the problem: the time discrete approximation is solved by…

We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…

At impact of a liquid drop on a solid surface an air bubble can be entrapped. Here we show that two competing effects minimize the (relative) size of this entrained air bubble: For large drop impact velocity and large droplets the inertia…