By William H., III Meeks, Joaquin Perez

ISBN-10: 0821869124

ISBN-13: 9780821869123

Meeks and Pérez current a survey of contemporary impressive successes in classical minimum floor concept. The category of minimum planar domain names in third-dimensional Euclidean area offers the focal point of the account. The evidence of the type depends upon the paintings of many at the moment energetic prime mathematicians, hence making touch with a lot of crucial ends up in the sphere. throughout the telling of the tale of the category of minimum planar domain names, the overall mathematician may well trap a glimpse of the intrinsic great thing about this idea and the authors' standpoint of what's taking place at this historic second in a really classical topic. This e-book contains an up to date travel via a few of the contemporary advances within the thought, equivalent to Colding-Minicozzi idea, minimum laminations, the ordering theorem for the distance of ends, conformal constitution of minimum surfaces, minimum annular ends with limitless overall curvature, the embedded Calabi-Yau challenge, neighborhood images at the scale of curvature and topology, the neighborhood detachable singularity theorem, embedded minimum surfaces of finite genus, topological category of minimum surfaces, strong point of Scherk singly periodic minimum surfaces, and awesome difficulties and conjectures

**Read Online or Download A survey on classical minimal surface theory PDF**

**Best differential geometry books**

Tight and taut manifolds shape a tremendous and distinctive classification of surfaces inside differential geometry. This ebook includes in-depth articles through specialists within the box in addition to an in depth and accomplished bibliography. This survey will open new avenues for extra examine and should be an incredible addition to any geometer's library.

**The geometry of Kerr black holes**

This distinctive monograph by way of a famous UCLA professor examines intimately the math of Kerr black holes, which own the homes of mass and angular momentum yet hold no electric cost. compatible for complex undergraduates and graduate scholars of arithmetic, physics, and astronomy in addition to expert physicists, the self-contained remedy constitutes an creation to fashionable recommendations in differential geometry.

Delivering an up to date evaluate of the geometry of manifolds with non-negative sectional curvature, this quantity offers a close account of the newest study within the sector. The lectures disguise quite a lot of themes akin to normal isometric crew activities, circle activities on certainly curved 4 manifolds, cohomogeneity one activities on Alexandrov areas, isometric torus activities on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, touch CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry.

**The Principle of Least Action in Geometry and Dynamics**

New variational equipment via Aubry, Mather, and Mane, came upon within the final two decades, gave deep perception into the dynamics of convex Lagrangian structures. This booklet indicates how this precept of Least motion appears to be like in various settings (billiards, size spectrum, Hofer geometry, sleek symplectic geometry).

- Singularities of Differentiable Maps: Volume II Monodromy and Asymptotic Integrals
- Curve evolution and image processing
- The Ricci Flow: An Introduction (Mathematical Surveys and Monographs)
- The Ricci Flow: An Introduction (Mathematical Surveys and Monographs)
- Algebras of Pseudodifferential Operators
- Geometry

**Additional resources for A survey on classical minimal surface theory**

**Sample text**

Singly-periodic Scherk surface with angle θ = π/2 (left), and its conjugate surface, the doubly-periodic Scherk surface (right). Images courtesy of M. Weber. Hoﬀman and White [92] gave a variational proof of the existence of a genusone helicoid. 21). The singly-periodic Scherk surfaces. 5 Left for the case θ = π/2. Discovered by Scherk [217] in 1835, these surfaces denoted by Sθ form a 1-parameter family of complete, embedded, genus-zero minimal surfaces in a quotient of R3 by a translation, and have four annular ends.

If e ∈ E(M ) is not a simple end (equivalently, if it is a limit point of E(M ) ⊂ [0, 1]), we will call it a limit end of M . When M has dimension 2, then an elementary topological analysis using compact exhaustions shows that an end e ∈ E(M ) is simple if and only if it 18 Throughout the paper, the word eventually for proper arcs means outside a compact subset of the parameter domain [0, ∞). 36 2 Basic results in classical minimal surface theory can be represented by a proper subdomain Ω ⊂ M with compact boundary which is homeomorphic to one of the following models: (a) S1 × [0, ∞) (this case is called an annular end).

5. Singly-periodic Scherk surface with angle θ = π/2 (left), and its conjugate surface, the doubly-periodic Scherk surface (right). Images courtesy of M. Weber. Hoﬀman and White [92] gave a variational proof of the existence of a genusone helicoid. 21). The singly-periodic Scherk surfaces. 5 Left for the case θ = π/2. Discovered by Scherk [217] in 1835, these surfaces denoted by Sθ form a 1-parameter family of complete, embedded, genus-zero minimal surfaces in a quotient of R3 by a translation, and have four annular ends.