9 papers · 1 filter
Hopf Reduction and Multiplicity-Resolved Endpoints for the Classical Willmore Flow of Hopf Tori
Mohameden Ahmedou, Ruben Jakob
We establish an exact parametrized reduction of the classical Willmore flow of Hopf tori in the round three-sphere to the spherical elastic flow. In Willmore-flow time the reductio…
Uniqueness of Finite-Time Varifold Limits for the Möbius-Invariant Willmore Flow
Mohameden Ahmedou, Ruben Jakob
We prove uniqueness of finite-time geometric endpoints for the Möbius-invariant Willmore flow in under uniform quantitative nonumbilicity. The multiplicity-counting…
Blow-up solutions for mean field equations with non-quantized singularities on Riemann surfaces with boundary
Mohameden Ahmedou, Zhengni Hu, Miaomiao Zhu
We study mean field equations with singular sources on a compact Riemann surface with boundary , subject to homogeneous Neumann boundary conditions: \[ -Δ_g v = ρ\left( \fra…
A degree-counting formula for a Keller-Segel equation on a surface with boundary
Mohameden Ahmedou, Zhengni Hu, Heming Wang
In this paper, we consider the following Keller-Segel equation on a compact Riemann surface with smooth boundary : \[ -Δ_g u = ρ\Big(\frac{V e^u}{\int_Σ V e^u \…
Blow-up solutions for the steady state of the Keller-Segel system on Riemann surfaces
Mohameden Ahmedou, Thomas Bartsch, Zhengni Hu
We study the following Neumann boundary problem related to the stationary solutions of the Keller-Segel system, a basic model of chemotaxis phenomena: \[ \left\{\begin{array}{ll} -…
Partial Blow-up Phenomena in the Toda System on Riemann Surfaces
Zhengni Hu, Mohameden Ahmedou, Thomas Bartsch
This work studies the partial blow-up phenomena for the Toda system on compact Riemann surfaces with smooth boundary. We consider the following coupled Liouville system wit…
Blow-up solutions for mean field equations with Neumann boundary conditions on Riemann surfaces
Zhengni Hu, Thomas Bartsch, Mohameden Ahmedou
On a compact Riemann surface with a smooth boundary , we consider the following mean field equations with Neumann boundary conditions: $$ -Δ_g u = λ\left(\frac…
On the Nirenberg problem on spheres: Arbitrarily many solutions in a perturbative setting
Mohameden Ahmedou, Mohamed Ben Ayed, Khalil El Mehdi
Given a smooth positive function on the standard sphere , we use Morse theoretical methods and counting index formulae to prove that, under generic conditio…
Nirenberg problem on high dimensional spheres: Blow up with residual mass phenomenon
Mohameden Ahmedou, Mohamed Ben Ayed, Khalil El Mehdi
In this paper, we extend the analysis of the subcritical approximation of the Nirenberg problem on spheres recently conducted in \cite{MM19, MM}. Specifically, we delve into the sc…