... 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...

- 17
- 176
- 0

... 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...

- 51
- 189
- 0

... 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...

- 62
- 188
- 0

... 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...

- 21
- 179
- 0

... 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...

- 44
- 184
- 0

... 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...

- 100
- 154
- 0

... (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...

- 30
- 173
- 0

... ——— , ** 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...

- 43
- 174
- 0

... ** 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...

- 25
- 91
- 0

... 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...

- 23
- 117
- 0

... 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...

- 35
- 80
- 0

... 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...

- 44
- 54
- 0

... 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...

- 37
- 79
- 0

... in ** the ** sense ** of ** Conley [17] for ** the ** ** curve ** ** shortening ** ﬂow We then deﬁne a Conley index h(Bα ) ** of ** Bα ** 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...

- 56
- 129
- 0

... 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...

- 34
- 204
- 0

Từ khóa:
Chính sách phát triển ngành sản xuất thép việt namTác động của chính sách tỷ giá đến thu hút vốn đầu tư trực tiếp nước ngoài ở việt nam (tt)Tài Liệu Tiếng Anh Cho Người Du LịchNâng cao năng lực cạnh tranh sản phẩm gỗ việt nam tại thị trường EU từ khi việt nam gia nhập WTO (tóm tắt)BÀI TẬP VÔ CƠ HAY VÀ KHÓ5 đề THI THỬ THPT CHUYÊN THOẠI NGỌC hầu lần 1 20175 đề THI THỬ THPT LƯƠNG THẾ VINH lần 1 2017Ebook Atlas of anatomic pathology Part 2genes the environment and diseaseHIỆN TƯỢNG SONG NGỮ của NGƯỜI PACÔ TRÊN BÌNH DIỆN cá NHÂNmau bao cao học phan foxproEbook Lange pathology flash cards (2nd edition) Part 1Ebook Introduction to sectional anatomy (3rd edition) Part 2Ebook Human anatomy physiology (9th edition) Part 1Ebook Medical microbiology Part 1Ebook Manual of botulinum toxin thera (2rd edition) Part 2Ebook Liver pathology Part 1Ebook Nelson’s pediatric antimicrobial therapy (20th edition) Part 2Ebook Nelson’s pediatric antimicrobial therapy (20th edition) Part 1Ebook MRI at a glance Part 2