Related papers: Rigidity and non-rigidity results for conformal im…
We establish an energy quantization result for sequences of Willmore surfaces when the underlying sequence of Riemann surfaces is degenerating in the moduli space. we notably exhibit a new residue which quantifies the potential loss of…
For smooth surfaces properly immersed in the unit ball of $\RR^n$ with density close to one and small Willmore energy, the optimal a priori estimate(bi-Lipschitz and $W^{2,2}$ parametrization)is provided. We also discuss the quantitative…
We prove a rigidity result in the sphere which allows us to generalize a result about smooth convex hypersurfaces in the sphere by Do Carmo-Warner to convex $C^2$-hypersurfaces. We apply these results to prove $C^{1,\beta}$-convergence of…
We will study the blowup behavior of a surface sequence immersed in $R^2$ with bounded Willmore functional and fixed genus.
We offer an alternative approach to the asymptotic rigidity of codimension-1 isometric immersions via quantitative rigidity estimates. We show that an immersion between compact manifolds $M$ and $N$ of dimensions $d$ and $d + 1$,…
We establish an asymptotic rigidity result for isometric immersions of codimension-1. Specifically, we consider a sequence of immersions from a compact $d$-dimensional manifold into a complete $(d+1)$-dimensional manifold whose elastic…
In this paper, for an immersion $f$ of an $n$-dimensional Riemannian manifold $M$ into $(n+d)$-Euclidean space we give a sufficient condition on $f$ so that, in case $d\leq 5$, any immersion $g$ of $M$ into $(n+d+1)$-Euclidean space that…
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…
We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric…
We consider the class of all conformal mappings from a compact Riemann surface into the threedimensional or fourdimensional Euclidean space. A sequence in this class with bounded Willmore functional is shown to have a sequence of conformal…
Functionals involving surface curvature are important across a range of scientific disciplines, and their extrema are representative of physically meaningful objects such as atomic lattices and biomembranes. Inspired in particular by the…
A new functional for simplicial surfaces is suggested. It is invariant with respect to Moebius transformations and is a discrete analogue of the Willmore functional. Minima of this functional are investigated. as an application a bending…
This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the…
We present a quantitative geometric rigidity estimate for special functions of bounded deformation in a planar setting generalizing the result by Friesecke, James, M\"uller obtained in nonlinear elasticity theory and the piecewise rigidity…
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…
In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactness of discrete multi-well energies associated with the…
Some classification results for closed surfaces in Berger spheres are presented. On the one hand, a Willmore functional for isometrically immersed surfaces into an homogeneous space $\mathbb{E}^{3}(\kappa,\tau)$ with isometry group of…
In this paper, we are going to show some rigidity results for complete open Riemannian manifolds with nonnegative scalar curvature. Without using the famous Cheeger-Gromoll splitting theorem we give a new proof to a rigidity result for…
We study isometric immersions of a Riemannian surface $(\Omega,\frak{g})$, where $\Omega \subset \mathbb{R}^2$, into $\mathbb{R}^3$. We consider their bending energy, i.e., the square of the $L^2$-norm of their second fundamental form,…
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…