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We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
Center manifold analysis can be used in order to investigate the stability of the stationary solutions of various PDEs. This can be done by considering the PDE as an ODE between certain Banach spaces ...
Abstract: We construct travelling wave graphs of the form $z=-ct+\phi(x)$, $\phi: x \in \mathbb{R}^{N-1} \mapsto \phi(x)\in \mathbb{R}$, $N \geq 2$, solutions to the $N$-dimensional forced mean curvat...
We generalize the second pinching theorem for minimal hypersurfaces in a sphere due to Peng-Terng, Wei-Xu, Zhang, and Ding-Xin to the case of hypersurfaces with small constant mean curvature. Let Mn b...
In this paper I study the constant mean curvature surface in asymp-totically flat 3-manifolds with general asymptotics. Under some weak condition, I prove that outside some compact set in the asymptot...
We consider n-dimensional hypersurfaces flowing by mean curvature flow with Neumann free boundary conditions supported on a smooth support surface. We show that the Hausdorff n-measure of the singula...
We extend the estimate obtained in [1] for the mean curvature of a cylindrically bounded proper submanifold in a product manifold with an Euclidean space as one factor to a general product ambient spa...
We define a transformation on harmonic maps N : M ! S2 from a Riemann surface M into the 2–sphere which depends on a parameter μ 2 C, the so–called μ–Darboux transformation.
This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg--Landau system which simulates inhomogeneous type II superconducting materials and three-dimens...

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