Related papers: Towards a constrained Willmore conjecture

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean…

This paper studies the regularity of constrained Willmore immersions into $\R^{m\ge3}$ locally around both "regular" points and around branch points, where the immersive nature of the map degenerates. We develop local asymptotic expansions…

We study some particular cases of Viterbo's conjecture relating volumes of convex bodies and actions of closed characteristics on their boundaries, focusing on the case of a Hamiltonian of classical mechanical type, splitting into summands…

In this article we encode Hadwiger's covering conjecture and Borsuk's partition conjecture into continuous functions defined on the spaces of convex bodies, propose a four-step program to approach them, and obtain some partial results.

We propose the study of a conformally invariant functional for surfaces of complex projective plane which is closely related to the classical Willmore functional. We show that minimal surfaces of complex projective plane are critical for…

We found a new formulation to the Euler-Lagrange equation of the Willmore functional for immersed surfaces in ${\R}^m$. This new formulation of Willmore equation appears to be of divergence form, moreover, the non-linearities are made of…

The unsigned p-Willmore functional introduced in \cite{mondino2011} generalizes important geometric functionals which measure the area and Willmore energy of immersed surfaces. Presently, techniques from \cite{dziuk2008} are adapted to…

We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. Our conjectures are based on experimental data that we derived by developing a numerical linear algebra and distributed…

We consider minimization problems of functionals given by the difference between the Willmore functional of a closed surface and its area, when the latter is multiplied by a positive constant weight $\Lambda$ and when the surfaces are…

In this paper we show a quantitative rigidity result for the minimizer of the Willmore functional among all projective planes in $\mathbb{R}^n$ with $n\ge 4$. We also construct an explicit counterexample to a corresponding rigidity result…

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

We present a reduction of the Hilbert-Smith conjecture in the case of the finite dimensional orbit space to some algebraic topology problems.

We present a conjecture about partitions, with a very elementary formulation.

We study immersed surfaces in $\mathbb{R}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary…

Using the reformulation in divergence form of the Euler-Lagrange equation for the Willmore functional as it was developed in "Analysis of the Willmore Functional" by T. Riviere (Invent. Math. 174), we study the limit of a local Palais-Smale…

We investigate surfaces with bounded L^p-norm of the fractional mean curvature, a quantity we shall refer to as fractional Willmore-type functional. In the subcritical case and under convexity assumptions we show how this…

We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harmonic surfaces in the sense of Chen, among others. We prove…

The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing together ideas from subjects like conformal geometry, partial…

Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…

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…