Search Results - "Palmer, Bennett"
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A version of Krust's theorem for anisotropic minimal surfaces
Published in Proceedings of the American Mathematical Society. Series B (31-03-2023)“…We generalize Krust’s theorem to an anisotropic setting by showing the following. If \Sigma is an anisotropic minimal surface in an axially symmetric normed…”
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Stable surfaces with constant anisotropic mean curvature and circular boundary
Published in Proceedings of the American Mathematical Society (01-11-2013)“…We show that for an axially symmetric anisotropic surface energy, only stable disc-type surfaces with constant anisotropic mean curvature bounded by a circle…”
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Higher order variations of constant mean curvature surfaces
Published in Calculus of variations and partial differential equations (01-12-2017)Get full text
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Rolling construction for anisotropic Delaunay surfaces
Published in Pacific journal of mathematics (01-02-2008)Get full text
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Stability of spherically confined free boundary drops with line tension
Published in Annals of global analysis and geometry (01-03-2020)“…We study the geometry of a stable drop of incompressible liquid constrained to lie in a spherical container. The energy functional is comprised of the surface…”
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Stability of anisotropic capillary surfaces between two parallel planes
Published in Calculus of variations and partial differential equations (01-03-2006)“…We study the stability of capillary surfaces without gravity for anisotropic free surface energies. For a large class of rotationally symmetric energy…”
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Symmetry breaking bifurcation of membranes with boundary
Published in Nonlinear analysis (01-01-2024)“…We use a bifurcation theory due to Crandall and Rabinowitz to show the existence of a symmetry breaking bifurcation of a specific one parameter family of…”
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Stability of the Wulff shape
Published in Proceedings of the American Mathematical Society (01-12-1998)“…We consider the functional of a hypersurface, given by a convex elliptic integrand with a volume constraint. We show that, up to homothety and translation, the…”
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The Euler–Helfrich functional
Published in Calculus of variations and partial differential equations (01-06-2022)“…We investigate equilibrium configurations for surface energies which contain the squared L 2 norm of the difference of the mean curvature H and the spontaneous…”
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Higher order variations of constant mean curvature surfaces
Published in Calculus of variations and partial differential equations (2017)“…We study the third and fourth variation of area for a compact domain in a constant mean curvature surface when there is a Killing field on R 3 whose normal…”
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Stability of Membranes
Published in The Journal of geometric analysis (01-11-2024)“…In Palmer and Pámpano (Calc Var Partial Differ Equ 61:79, 2022), the authors studied a particular class of equilibrium solutions of the Helfrich energy which…”
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ON THE GAUSSIAN CURVATURE OF MAXIMAL SURFACES AND THE CALABI–BERNSTEIN THEOREM
Published in The Bulletin of the London Mathematical Society (01-07-2001)“…In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz– Minkowski space L3 is introduced. The approach is based on an…”
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Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries
Published in Journal of nonlinear science (01-02-2021)“…We study critical surfaces for a surface energy which contains the squared L 2 norm of the difference of the mean curvature H and the spontaneous curvature c o…”
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Area minimization among marginally trapped surfaces in Lorentz–Minkowski space
Published in Calculus of variations and partial differential equations (01-07-2011)“…We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz–Minkowski space. The areas of these surfaces are…”
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A duality result between the minimal surface equation and the maximal surface equation
Published in Anais da Academia Brasileira de Ciências (01-06-2001)“…In this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's theorem on…”
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Axially symmetric volume constrained anisotropic mean curvature flow
Published in Calculus of variations and partial differential equations (01-07-2014)“…We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary…”
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Anisotropic bending energies of curves
Published in Annals of global analysis and geometry (01-03-2020)“…We study the shape of an elastic rod subject to both bending and twisting, when the rod’s resistance to bending depends on the direction of the deformation. In…”
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Anisotropic Umbilic Points and Hopf's Theorem for Surfaces with Constant Anisotropic Mean Curvature
Published in Indiana University mathematics journal (01-01-2010)“…We show that for elliptic parametric functionals whose Wulff shape is smooth and has strictly positive curvature, any surface with constant anisotropic mean…”
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Equilibrium shapes of cylindrical rotating liquid drops
Published in Boletim da Sociedade Brasileira de Matemática (01-12-2015)“…We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the vertical axis. We restrict…”
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Equilibria for anisotropic surface energies with wetting and line tension
Published in Calculus of variations and partial differential equations (01-03-2012)“…We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic…”
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