Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks " doc

... of s, a standard argument then gives(II.1.16).Annals of Mathematics The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains By Tobias H. Colding ... tubular neighborhoods of curves lying in the intersection of the surface and the boundary of an extrinsic ball. These domains arise naturally in our main result and are unfortunately somewhat more ... proved estimates for the total curvature and area of stable sectors. A stable sector in the sense of [CM3], [CM4] is a stable subset of a minimal surface given as half of a normal tubular neighborhood...

... ,(II.1.12)E(χ1)+SR1∩{χ1<1} |A| 2≤˜CR1/r1,(II.1.13)E(χ)+SR1∩{χ<1} |A| 2≤˜C (R1/r1+ m) .(II.1.14)Annals of Mathematics The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks By Tobias ... describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closedRiemannian 3-manifold. The key for understanding such surfaces is to un-derstand the local structure ... facts about minimal surfaces in a slab will be used:• Stable surfaces in a slab must be graphical away from their boundary(see Lemma I.0.9 below).• The maximum principle, and catenoid foliations...

... was proved in [G-S1] that there is a coarse moduli space of δ-semistabletensors.Now we go to our second main concept, that of a g-sheaf. It will appearas a particular case of Lie algebra ... on thesenumerical invariants, and V is a fixed vector space of dimension PE(m), thusdepending only on the invariants. We have already seen that a g-sheaf can bedescribed as a tensor in the ... Spec C. In this section and the following we are going to make use of the category of complex analytic spaces. For a scheme Y , we denote by Yan the associated complex analytic space ([SGA1, XII],...

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