인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

완효성 비료와 4종복비의 혼용 시용이 팔레놉시스의 생육에 미치는 효과

This is the first of a series of three papers which provide proofs of results announced recently in arXiv:1210.7494.

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Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities

This article considers the existence and regularity of Kahler{Einstein metrics on a compact Kahler manifold M with edge singularities with cone angle 2 along a smooth divisor D. We prove existence of such metrics with negative, zero and some positive cases for all cone angles 2 2 . The results in the positive case parallel those in the smooth case. We also establish that solutions of this problem are polyhomogeneous, i.e., have a complete asymptotic expansion with smooth coecients along D for all 2 < 2 .

Kahler-Einstein metrics with edge singularities

Let $X$ be a non-singular compact Kahler manifold, endowed with an effective divisor $D=\sum{(1-\beta_k) Y_k}$ having simple normal crossing support, and satisfying $\beta_k \in (0, 1)$. The natural objects one has to consider in order to explore the differential-geometric properties of the pair $(X,D)$ are the so-called metrics with conic singularities. In this article, we complete our earlier work concerning the Monge-Ampere equations on $(X,D)$ by establishing Laplacian and $\mathscr{C}^{2,\alpha,\beta}$ estimates for the solution of these equations regardless of the size of the coefficients $0 \lt \beta_k \lt 1$. In particular, we obtain a general theorem concerning the existence and regularity of Kahler–Einstein metrics with conic singularities along a normal crossing divisor.

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Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors

We prove the existence of non-positively curved Kahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact Kahler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kahler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.

/pdf/metrics-with-cone-singularities-along-normal-crossing-1ka8j1knd2.pdf

Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical class K (X) defines an ample -line bundle, and satisfying the conditions G (1) and S (2). Our main result says that X admits a Kahler-Einstein metric iff X has semi-log canonical singularities i.e. iff X is a stable variety in the sense of Kollar-Shepherd-Barron and Alexeev (whose moduli spaces are known to be compact). By definition a Kahler-Einstein metric in this singular context simply means a Kahler-Einstein on the regular locus of X with volume equal to the algebraic volume of K (X) , i.e. the top intersection number of K (X) . We also show that such a metric is uniquely determined and extends to define a canonical positive current in c (1)(K (X) ). Combined with recent results of Odaka our main result shows that X admits a Kahler-Einstein metric iff X is K-stable, which thus confirms the Yau-Tian-Donaldson conjecture in this general setting of (possibly singular) canonically polarized varieties. More generally, our results are shown to hold in the setting of log minimal varieties and they also generalize some prior results concerning Kahler-Einstein metrics on quasi-projective varieties.

Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs

We investigate the holonomy group of singular Kahler-Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the number of connected components, a Bochner principle for holomorphic tensors, and a connection between irreducibility of holonomy representations and stability of the tangent sheaf are established. As a consequence, known decompositions for tangent sheaves of varieties with trivial canonical divisor are refined. In particular, we show that up to finite quasi-etale covers, varieties with strongly stable tangent sheaf are either Calabi-Yau or irreducible holomorphic symplectic. These results form one building block for Horing-Peternell's recent proof of a singular version of the Beauville-Bogomolov Decomposition Theorem.

https://msp.org/gt/2019/23-4/gt-v23-n4-p08-s.pdf

Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups

In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier ideal sheaves, which generalizes the algebraic case studied by Howald. In the second part, almost entirely independent of the first one, we generalize the notion of the adjoint ideal sheaf used in algebraic geometry to the analytic setting. This enables us to give an analogue of Howald’s theorem for adjoint ideals attached to monomial ideals. Finally, using the local Ohsawa–Takegoshi–Manivel theorem, we prove the existence of the so-called generalized adjunction exact sequence, which enables us to recover a weak version of the global extension theorem of Manivel, for compact Kahler manifolds.

Henri Guenancia

Papers

Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors

Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs

Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups

Toric plurisubharmonic functions and analytic adjoint ideal sheaves