Related papers: The viscosity method for min-max free boundary min…

A two-dimensional steady problem of a potential free-surface flow of an ideal incompressible fluid caused by a singular sink is considered. The sink is placed at the horizontal bottom of the fluid layer. With the help of the Levi-Civita…

On the two-sphere $\Sigma$, we consider the problem of minimising among suitable immersions $f \,\colon \Sigma \rightarrow \mathbb{R}^3$ the weighted $L^\infty$ norm of the mean curvature $H$, with weighting given by a prescribed ambient…

Here we continue the investigation of the M\"obius-invariant Willmore flow (MIWF), starting to move in arbitrary smooth and umbilic-free initial immersions $F_0$ which map some fixed compact torus $\Sigma$ into $\mathbb{R}^n$ respectively…

Let $M$ be a compact Riemannian manifold of nonnegative Ricci curvature and $\Sigma$ a compact embedded 2-sided minimal hypersurface in $M$. It is proved that there is a dichotomy: If $\Sigma$ does not separate $M$ then $\Sigma$ is totally…

We consider the relationship of the geometry of compact Riemannian manifolds with boundary to the first nonzero eigenvalue sigma_1 of the Dirichlet-to-Neumann map (Steklov eigenvalue). For surfaces Sigma with genus gamma and k boundary…

We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a…

Let $(M,g)$ be a compact, smooth Riemannian manifold and $\{u_h\}$ be a sequence of $L^2$-normalized Laplace eigenfunctions that has a localized defect measure $\mu$ in the sense that $ M \setminus \text{supp}(\pi_* \mu) \neq \emptyset$…

Let $(\Sigma,g)$ be a compact Riemann surface with smooth boundary $\partial\Sigma$, $\Delta_g$ be the Laplace-Beltrami operator, and $h$ be a positive smooth function. Using a min-max scheme introduced by Djadli-Malchiodi (2006) and Djadli…

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…

We introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical…

In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional $$ \int_{\Omega}\left(|\nabla\mathbf{u}|^2+\frac2p|\mathbf{u}|^p\right),\quad…

We show that for a generic $8$-dimensional Riemannian manifold with positive Ricci curvature, there exists a smooth minimal hypersurface. Without the curvature condition, we show that for a dense set of 8-dimensional Riemannian metrics…

In a Hilbert space setting $\mathcal H$, given $\Phi: \mathcal H \to \mathbb R$ a convex continuously differentiable function, and $\alpha$ a positive parameter, we consider the inertial system with Asymptotic Vanishing Damping…

If $\psi:M^n\to \mathbb{R}^{n+1}$ is a smooth immersed closed hypersurface, we consider the functional $\mathcal{F}_m(\psi) = \int_M 1 + |\nabla^m \nu |^2 \, d\mu$, where $\nu$ is a local unit normal vector along $\psi$, $\nabla$ is the…

Let $\Sigma$ be a closed, embedded, oriented hypersurface in a closed oriented Riemannian manifold $N$. Under a lower bound on the Ricci curvature and an upper bound on the sectional curvature of $N$, we establish a lower bound for the…

Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary(IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction(FSI) in such systems,…

In this work, we consider $M=(\mathbb{B}^3_r,\bar{g})$ as the Euclidean three-ball with radius $r$ equipped with the metric $\bar{g}=e^{2h}\left\langle , \right\rangle$ conformal to the Euclidean metric. We show that if a free boundary CMC…

We prove area estimates for stable capillary $cmc$ (minimal) hypersurfaces $\Sigma$ with nonpositive Yamabe invariant that are properly immersed in a Riemannian $n$-dimensional manifold $M$ with scalar curvature $R^M$ and mean curvature of…

In this paper we study $\varphi$-minimal surfaces in $\mathbb{R}^3$ when the function $\varphi$ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in $\mathbb{R}^2$. We…

Let $M$ be a 5 dimensional Riemannian manifold with $Sec_M\in[0,1]$, $\Sigma$ be a locally conformally flat hypersphere in $M$ with mean curvature $H$. We prove that, there exists $\varepsilon_0>0$, such that $\int_\Sigma (1+H^2)^2 \ge…