Minkowski Geometry—Some Concepts and Recent Developments
From MaRDI portal
Publication:5050924
DOI10.1007/978-3-030-86695-2_3zbMath1506.52001OpenAlexW4212899621MaRDI QIDQ5050924
Publication date: 18 November 2022
Published in: Surveys in Geometry I (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-030-86695-2_3
Geometry and structure of normed linear spaces (46B20) Surfaces in Euclidean and related spaces (53A05) Curves in Euclidean and related spaces (53A04) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Minkowski geometries in nonlinear incidence geometry (51B20) Research exposition (monographs, survey articles) pertaining to convex and discrete geometry (52-02) Research exposition (monographs, survey articles) pertaining to geometry (51-02)
Cites Work
- A new construction of Radon curves and related topics
- Birkhoff-James orthogonality of linear operators on finite dimensional Banach spaces
- Cassini curves in normed planes
- On reduced triangles in normed planes
- Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I.
- Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II.
- Iteration of involutes of constant width curves in the Minkowski plane
- Minsum location extended to gauges and to convex sets
- Geometric properties of a sine function extendable to arbitrary normed planes
- Angles in normed spaces
- A quantitative program for Hadwiger's covering conjecture
- A characterization of normed spaces among metric spaces
- Tangent segments and orthogonality types in normed planes
- Geometry where direction matters -- or does it?
- On intrinsic geometry of surfaces in normed spaces
- On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces
- On Miquel's theorem and inversions in normed planes
- Minsum hyperspheres in normed spaces
- Measurements of differences between orthogonality types
- On angular measures in Minkowski planes
- Geometry of simplices in Minkowski spaces
- Geometric constants for quantifying the difference between orthogonality types
- Minimum chords in Minkowski planes
- From symplectic measurements to the Mahler conjecture
- Complete sets need not be reduced in Minkowski spaces
- On the geometry of Minkowski planes
- Duality of gauges and symplectic forms in vector spaces
- Quantitative characterization of the difference between Birkhoff orthogonality and isosceles orthogonality
- A characterization of normed spaces
- General embedding problems and two-distance sets in Minkowski planes
- The Ptolemy and Zbăganu constants of normed spaces
- Semi-indefinite inner product and generalized Minkowski spaces
- Geometric dilation of closed curves in normed planes
- \(I\)-measures in Minkowski planes
- On regular 4-coverings and their application for lattice coverings in normed planes
- Halving circular arcs in normed planes
- The Fermat problem in Minkowski spaces
- Geometrical properties of the Fermat-Weber problem
- Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
- On plane Minkowski geometry
- Minimal surfaces, crystals, shortest networks, and undergraduate research
- Geometric methods and optimization problems
- Median hyperplanes in normed spaces -- a survey
- Locating lines and hyperplanes. Theory and algorithms
- Two characterizations of smooth norms
- Parametrized plane curves, Minkowski caustics, Minkowski vertices and conservative line fields
- Some remarkable lines of triangles in real normed spaces and characterizations of inner product structures
- On equilateral simplices in normed spaces
- Billiards in Finsler and Minkowski geometries
- The ratios of diameter and width of reduced and of complete convex bodies in Minkowski spaces
- Approximate Birkhoff-James orthogonality in the space of bounded linear operators
- On symmetry of Birkhoff-James orthogonality of linear operators
- Angle measures, general rotations, and roulettes in normed planes
- A perimeter-based angle measure in Minkowski planes
- Closed cycloids in a normed plane
- Approximate symmetry of Birkhoff orthogonality
- Is a complete, reduced set necessarily of constant width?
- Monge points, Euler lines, and Feuerbach spheres in Minkowski spaces
- Conics in Minkowski geometries
- On Legendre curves in normed planes
- Uniqueness of circumcenters in generalized Minkowski spaces
- The Fermat--Torricelli problem in normed planes and spaces
- Characterizations of inner product spaces
- Controlling curvature in Minkowski planes
- von Neumann-Jordan constant and uniformly non-square Banach spaces
- On asymptotic volume of Finsler tori, minimal surfaces in normed spaces, and symplectic filling volume.
- The concepts of triangle orthocenters in Minkowski planes
- An angle in Minkowski space
- Equiframed curves -- a generalization of Radon curves
- Orthocenters in real normed spaces and the Euler line
- Smallest maximal snakes of translates of convex domains
- Erdös distance problems in normed spaces
- Bounded representation and radial projections of bisectors in normed spaces
- Discrete cycloids from convex symmetric polygons
- Triangles in convex distance planes
- On curvature of surfaces immersed in normed spaces
- Differential geometry of immersed surfaces in three-dimensional normed spaces
- Universal points of convex bodies and bisectors in Minkowski spaces
- Reduced convex bodies in finite dimensional normed spaces: a survey
- Median spheres: Theory, algorithms, applications
- The inverse problem on roulettes in normed planes
- Concepts of curvatures in normed planes
- Surface immersions in normed spaces from the affine point of view
- Open research areas in distance geometry
- Generalized von Neumann-Jordan constant and its relationship to the fixed point property
- Operator norm attainment and Birkhoff-James orthogonality
- Approximate Roberts orthogonality
- Ball convex bodies in Minkowski spaces
- On a conjecture of H. Hadwiger
- Pseudo-Minkowski differential geometry
- Classical curve theory in normed planes
- Observations on circumcenters in normed planes
- Combinatorial distance geometry in normed spaces
- The Feuerbach circle and orthocentricity in normed places
- Embedding metric spaces into normed spaces and estimates of metric capacity
- Tangent segments in Minkowski planes
- A metric characterization of normed linear spaces
- Antinorms and Radon curves
- A property of planar convex bodies
- The converse to the four vertex theorem
- Excursions into combinatorial geometry
- The geometry of Minkowski spaces -- a survey. II.
- On inner products in linear, metric spaces
- The foundations of Minkowskian geometry
- Konvexe Mittelpunktsbereiche und normierte Räume
- Some topics in differential geometry of normed spaces
- On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces
- Involutes of polygons of constant width in Minkowski planes
- Discrete Geometry in Minkowski Spaces
- Voronoi Diagrams and Delaunay Triangulations
- Bounds for Minkowski Billiard Trajectories in Convex Bodies
- Circle configurations in strictly convex normed planes
- Concurrent and parallel chords of spheres in normed linear spaces
- Minkowskian rhombi and squares inscribed in convex Jordan curves
- On Zindler Curves in Normed Planes
- Conics in normed planes
- An Application of Elementary Geometry in Functional Analysis
- Research Problems in Discrete Geometry
- Ein Problem der zweidimensionalen Minkowskischen Geometrie
- A Geometrical Approach to the Second-Order Linear Differential Equation
- Angle Measures and Bisectors in Minkowski Planes
- Halving closed curves in normed planes and related inequalities
- Angle Bisectors in Normed Linear Spaces
- On Generalizations of Conics and on a Generalization of the Fermat- Torricelli Problem
- On a generalization of the sine function
- Covering unit spheres and balls of normed spaces by smaller balls
- On a cosine function defined for smooth normed spaces
- Orthogonality in Generalized Minkowski Spaces
- Optimal constants in normed planes
- Duality of caustics in Minkowski billiards
- Bodies of Constant Width
- THE ROSENTHAL–SZASZ INEQUALITY FOR NORMED PLANES
- Convex analysis in normed spaces and metric projections onto convex bodies
- Regular polygons in taxicab geometry
- Asymptotic Geometric Analysis, Part I
- History of Banach Spaces and Linear Operators
- Euclidean Distance Geometry and Applications
- Convex Bodies The Brunn-MinkowskiTheory
- Dual spheres have the same girth
- On area and side lengths of triangles in normed planes
- On inscribing and circumscribing hexagons
- Equilateral Sets in Minkowski Spaces
- The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces
- On Bisectors in Normed Spaces
- On the class of Banach spaces with James constant 2
- Some Characterizations of Inner-Product Spaces
- The Isoperimetric Problem in the Minkowski Plane
- The geometry of Finsler spaces
- The Isoperimetric Problem for Minkowski Area
- A Property of Minkowskian Circles
- Geometry of cuts and metrics
- Orthogonality in normed linear spaces
- Simplexes with prescribed edge lengths in Minkowski and Banach spaces
- On bisectors in Minkowski normed spaces
- Voronoi diagrams for convex polygon-offset distance functions
- The geometry of Minkowski spaces -- a survey. I
- On James and Jordan-von Neumann constants of Lorentz sequence spaces
- Gauge distances and median hyperplanes
- Median and center hyperplanes in Minkowski spaces -- a unified approach
- On covering functionals of convex bodies
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item