Variational Methods for Discrete Geometric Functionals

DOI10.1007/978-3-030-31351-7_5OpenAlexW3014310120MaRDI QIDQ3300536

Henrik Schumacher, Max Wardetzky

Publication date: 29 July 2020

Published in: Handbook of Variational Methods for Nonlinear Geometric Data (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-31351-7_5

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Cites Work

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• Sobolev metrics on shape space of surfaces
• Convergence of curvatures in secant approximations
• Curvature weighted metrics on shape space of hypersurfaces in \(n\)-space
• Second fundamental measure of geometric sets and local approximation of curvatures
• Minimal surfaces from circle patterns: geometry from combinatorics
• On the convergence of metric and geometric properties of polyhedral surfaces
• Completeness properties of Sobolev metrics on the space of curves
• Uniform convergence of discrete curvatures from nets of curvature lines
• Properties of Sobolev-type metrics in the space of curves
• On discrete Dirichlet and Plateau problems
• An introduction to \(\Gamma\)-convergence
• On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
• Variational convergence of discrete minimal surfaces
• On the numerical approximation of unstable minimal surfaces with polygonal boundaries
• The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data
• Sobolev metrics on shape space. II: Weighted Sobolev metrics and almost local metrics
• On the curvature of piecewise flat spaces
• Extensional \textit{Elastica} in large deformation as \(\Gamma \)-limit of a discrete 1D mechanical system
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• On the angular defect of triangulations and the pointwise approximation of curvatures
• Constructing reparameterization invariant metrics on spaces of plane curves
• Discrete differential geometry
• Generalized curvatures
• Riemannian geometries on spaces of plane curves
• Critical points and curvature for embedded polyhedra
• Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
• Why Use Sobolev Metrics on the Space of Curves
• GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES
• Almost Local Metrics on Shape Space of Hypersurfaces inn-Space
• Epi-convergence of discrete elastica
• Regularity of Minimal Surfaces
• Discrete Solution of the Plateau Problem and its Convergence
• The discrete Plateau Problem: Algorithm and numerics
• The discrete plateau problem: Convergence results
• Computing Discrete Minimal Surfaces and Their Conjugates
• Variational Analysis
• Solution of the Problem of Plateau
• A Glimpse into Discrete Differential Geometry
• Convergence of Hencky-Type Discrete Beam Model to Euler Inextensible Elastica in Large Deformation: Rigorous Proof
• The discrete Douglas problem: convergence results
• Euler elastica as a Γ-limit of discrete bending energies of one-dimensional chains of atoms
• Lipschitz conformal immersions from degenerating Riemann surfaces with L2-bounded second fundamental forms
• On the Gamma-convergence of some polygonal curvature functionals
• Restricted delaunay triangulations and normal cycle
• Boundary regularity and embedded solutions for the oriented Plateau problem