IMPLICITATION DE SURFACES RATIONNELLES

Tài liệu Đề tài " Moduli spaces of surfaces and real structures " doc

Tài liệu Đề tài
... points and moduli spaces of surfaces of general type, Compositio Math 61 (1987), 81–102 , Connected components of moduli spaces, J Differential Geom 24 (1986), 395–399 , Moduli and classification of ... seminar, E Klassen MODULI SPACES OF SURFACES AND REAL STRUCTURES 591 and V Kharlamov for a useful conversation, V Kulikov and Sandro Manfredini for pointing out some nonsense, Sandro again for the ... and it is well known that on a connected component of the moduli space the differentiable structure remains fixed (we use for this result the slogan DEF ⇒ DIFF) MODULI SPACES OF SURFACES AND REAL...
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Tài liệu Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains " doc

Tài liệu Đề tài
... Annals of Mathematics, 160 (2004), 523–572 The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains By Tobias H Colding and William P Minicozzi II* Introduction ... from the boundary Here small means contained in a small ball 527 PLANAR DOMAINS A “pair of pants” (in bold) Graphical annuli (dotted) separate the “pairs of pants” Figure 4: Decomposing the Riemann ... next two theorems are crucial for what we call the pairs of pants decomposition” of embedded minimal planar domains, recall the following prime examples of such domains: Minimal graphs (over...
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Tài liệu Đề tài " On the K2 of degenerations of surfaces and the multiple point formula " pptx

Tài liệu Đề tài
... X1 and X2 meeting along a conic If there are THE K OF DEGENERATIONS OF SURFACES 361 other components, then there is a component X meeting all the rest along a line Thus, the hyperplane section ... As a consequence of Theorem 5.20 and of Lemma 5.21, all this proves the statement about the components of X and their intersection in codimension one It remains to prove the final part of the statement ... that the contribution to c of each such point is purely local In other words, c= cx x where x varies in the set of Rn - and Sn -points of X and where cx is the contribution at x to the computation...
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Tài liệu Đề tài " The topological classification of minimal surfaces in R3 " pptx

Tài liệu Đề tài
... description of any properly embedded minimal surface in terms of the ordering of the ends, the parity of the middle ends, the genus of each end - zero or in nite - and the genus of the surface This topological ... carried out independently of the other planes since the modified plane is contained in the union of the components of W that intersect P and when P intersects W ∈ W, then no other plane in P intersects ... indexed plane in each of these slabs Next remove all of the odd indexed planes from P and reindex the remaining ones by N in an order preserving manner TOPOLOGICAL CLASSIFICATION OF MINIMAL SURFACES...
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Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected " pdf

Đề tài
... Annals of Mathematics, 160 (2004), 573–615 The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected By Tobias H Colding and William P Minicozzi II* Introduction ... The space of embedded minimal surfaces of fixed genus in a 3manifold I; Estimates off the axis for disks, Ann of Math 160 (2004), 27–68; math.AP/0210106 [CM4] ——— , The space of embedded minimal ... 3-manifold III; Planar domains, Ann of Math 160 (2004), 523–572; math.AP/0210141 [CM6] ——— , The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus, in preparation...
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Đề tài " The stable moduli space of Riemann surfaces: Mumford’s conjecture " ppt

Đề tài
... model of the) moduli space of Riemann surfaces of topological type F The connected component Diff (F ) of the identity acts freely on (F ) with orbit space (F ), the Teichm¨ller space The projection ... Annals of Mathematics, 165 (2007), 843–941 The stable moduli space of Riemann surfaces: Mumford’s conjecture By Ib Madsen and Michael Weiss* Abstract D Mumford conjectured in [33] that the rational ... where the source of π ψ is the disjoint union of the sources of π and ψ (See the remark just below.) To make the monoid structure explicit in the case of the target, we introduce hW ∨ hW and the...
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Đề tài " Growth of the number of simple closed geodesics on hyperbolic surfaces " docx

Đề tài
... (L), the number of simple closed geodesics of length ≤ L on a complete hyperbolic surface X of finite area We also study the frequencies of different types of simple closed geodesics on X and their ... alternative proof In a sequel, we give a different proof of the growth of the number of simple closed geodesics by using the ergodic properties of the earthquake flow on PMg,n , the bundle of measured ... relationship with the Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces Simple closed geodesics Let cX (L) be the number of primitive closed geodesics of length ≤ L on X The...
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Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks " doc

Đề tài
... ——— , The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus, in preparation [CM8] ——— , Embedded minimal disks, in Minimal surfaces (MSRI , 2001), Clay Mathematics ... π In either case the separation w = π A multi-valued minimal graph is a multi-valued graph of a function u satisfying the minimal surface equation GRAPHICAL OFF THE AXIS 29 x3 -axis One half ... Annals of Mathematics, 160 (2004), 27–68 The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks By Tobias H Colding and William P Minicozzi...
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Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Estimates off the axis for disks " pdf

Đề tài
... space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks, Ann of Math 160 (2004), 27–68; math.AP/0210106 [CM4] ——— , The space of embedded minimal surfaces ... surfaces of fixed genus in a 3-manifold III; Planar domains, Ann of Math., to appear; math.AP/0210141 [CM5] ——— , The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally ... connected, Ann of Math., to appear; math.AP/0210119 [CM6] ——— , The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus, in preparation [CM7] ——— , Embedded minimal disks, in...
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Đề tài " On integral points on surfaces " docx

Đề tài
... that some condition on the intersection numbers (Di Dj ) is needed (see Ex 1.1) ON INTEGRAL POINTS ON SURFACES 707 An application of Theorem concerns the points on a curve which are integral and ... of regular functions on C with at most poles of order N at the given points Then, going to an infinite subsequence {Pi } of ON INTEGRAL POINTS ON SURFACES 715 the integral points on C, we may assume ... Mathematics, 160 (2004), 705–726 On integral points on surfaces By P Corvaja and U Zannier Abstract We study the integral points on surfaces by means of a new method, relying on the Schmidt Subspace Theorem...
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Đề tài " Minimal surfaces from circle patterns: Geometry from combinatorics " ppt

Đề tài
... 231–264 Minimal surfaces from circle patterns: Geometry from combinatorics By Alexander I Bobenko∗ , Tim Hoffmann∗∗ , and Boris A Springborn∗∗* Introduction The theory of polyhedral surfaces ... such a Gauss map MINIMAL SURFACES FROM CIRCLE PATTERNS 233 This definition of discrete minimal surfaces leads to a construction method for discrete S-isothermic minimal surfaces from discrete holomorphic ... covered by the neighboring circles It is normally 2π for 255 MINIMAL SURFACES FROM CIRCLE PATTERNS interior circles, but it differs for circles on the boundary or for circles where the pattern...
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Đề tài " Removability of point singularities of Willmore surfaces " pdf

Đề tài
... Annals of Mathematics, 160 (2004), 315–357 Removability of point singularities of Willmore surfaces ¨ By Ernst Kuwert and Reiner Schatzle* Abstract We investigate point singularities of Willmore surfaces, ... again a smooth Willmore surface, but with a possible point singularity at the origin The purpose of this article is to study unit density point singularities of general Willmore surfaces in codimension ... limit of the line integral around the point singularity of this 1-form From this we conclude in Lemma 4.2 that the residues of a closed Willmore surface with finitely many point singularities of...
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Đề tài " Random k-surfaces " doc

Đề tài
... called k-surfaces The “2-dimensional” analog of the unit tangent bundle with the geodesic flow is a “space of pointed k-surfaces , which can be considered as the space of germs of complete k-surfaces ... previous section actually codes for the space of k-surfaces Conclusion We summarise our constructions and prove our main result, Theorem 3.2.1 RANDOM K-SURFACES 107 I would like to thank W Goldman ... various ways to construct k-surfaces In Section 6.3, we summarise results of [1] which allow us to obtain k-surfaces as solutions of an asymptotic Plateau problem Since k-surfaces are solutions...
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Đề tài " Curve shortening and the topology of closed geodesics on surfaces " potx

Đề tài
... in the sense of Conley [17] for the curve shortening flow We then define a Conley index h(Bα ) of and use standard variational arguments to conclude that nontriviality of the Conley index of ... p/q CURVE SHORTENING AND GEODESICS 1207 for certain constants c± (θ), at least one of which is nonzero If one of these constants vanishes then ϕθ is again a solution of Hill’s equation and therefore ... number of such local continuations will take one from θ = to θ = We will therefore now describe the construction of the tubular neighborhoods of the γθ and the local continuations of the fillings...
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Đề tài " The Calabi-Yau conjectures for embedded surfaces " potx

Đề tài
... and THE CALABI-YAU CONJECTURES FOR EMBEDDED SURFACES 235 kg for the two boundary terms in the Gauss-Bonnet theorem for the annulus Γi (both are uniformly bounded; γi kg is after all just the ... THE CALABI-YAU CONJECTURES FOR EMBEDDED SURFACES 213 The assumption of a lower bound for the supremum of the sum of the −2 squares of the principal curvatures, i.e., supBr0 |A|2 > r0 , in the ... the cone property (1) and, therefore, we get a bound for the sum of the radii si of these balls si ≤ C0 R/cin (2.33) i Combining this with the chord arc property (5) then gives a bound for the...
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