On Poincaré's isoperimetric problem for simple closed geodesics

DOI10.1016/0022-1236(81)90091-4zbMath0469.58007OpenAlexW1982782407MaRDI QIDQ1157059

Melvyn S. Berger, Enrico Bombieri

Publication date: 1981

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(81)90091-4

zbMATH Keywords

Poincare's isoperimetric variational problem for simple closed geodesicssmooth ovaloid in 3-space

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items

Analytical mini-max methods for Hamiltonian brake orbits of prescribed energy, Sur le volume minimal de ${R}\sp 2$, Geodesics, soap bubbles and pattern formation in Riemannian surfaces, SHARP POINCARÉ–SOBOLEV INEQUALITIES AND THE SHORTEST LENGTH OF SIMPLE CLOSED GEODESICS ON A TOPOLOGICAL TWO SPHERE, Geodesics and soap bubbles in surfaces

Cites Work

• On the oriented Plateau problem
• Regularity theory for almost minimal currents
• Existence of non-self-intersecting closed geodesic of general elliptic type on surfaces, close to a sphere
• On the isoperimetric inequality on surfaces of variable Gaussian curvature
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Three theorems on manifolds with bounded mean curvature
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item