Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

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In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

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From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

Springer2024

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

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2024

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Band Gap Renormalization at Different Symmetry Points in Perovskites

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We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole-Hopf solution of the KPZ equati ...

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The Allen-Cahn equation with generic initial datum

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We consider the Allen-Cahn equation ?(t)u - ?u = u - u(3) with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets o ...

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Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

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