Related papers: Blowing-up points on l.c. K. manifolds
This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. In particular, this paper answers an open question posed by Guckenheimer and Scheper [SIAM J. Appl. Dyn. Syst. 10-1…
In this paper, we consider a class of balanced manifolds and provide a proof of a problem proposed by Silva-that compact complex manifolds that are Kahler outside an analytic subset are balanced. Next, as a special case of this theorem, we…
In this paper, we study the blow-up phenomena on the $\alpha_k$-harmonic map sequences with bounded uniformly $\alpha_k$-energy, denoted by $\{u_{\alpha_k}: \alpha_k>1 \quad \mbox{and} \quad \alpha_k\searrow 1\}$, from a compact Riemann…
Utilizing a splitting of geometric flows on surfaces introduced by Buzano and Rupflin, we present a general scheme to prove blow up criteria for such geometric flows. A vital ingredient is a new compactness theorem for families of metrics…
We study conjectures on the dimension of linear systems on the blow-up of P^2 and P^3 at points in very general position. We provide algorithms and Maple codes based on these conjectures.
We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…
A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kaehler metric of constant scalar curvature on the blow-up according to…
We investigate blow-up properties for the initial-boundary value problem of a Keller-Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller-Segel model, we first…
We partially answer a question raised by Kiselev and Zlatos in \cite{MR2180809}; in the generalized dyadic model of the Euler equation, a blow-up of $H^{1/3+\delta}$-norm occurs. We recover a few previous blow-up results for various related…
We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding results for mean curvature flow in Euclidean space were proven by…
Given a symplectic manifold (M, {\omega}) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L. Furthermore, we show that if M admits an anti-symplectic involution…
We prove a theorem of Leray-Hirsch type and give an explicit blow-up formula for Dolbeault cohomology on (\emph{not necessarily compact}) complex manifolds. We give applications to strongly $q$-complete manifolds and the…
Given a compact Chern-Ricci flat balanced orbifold, we show that its blow-up at a finite family of smooth points admits constant Chern scalar curvature balanced metrics, extending Arezzo-Pacard's construction to the balanced setting.…
A locally conformally K\"ahler (LCK) manifold is a complex manifold $M$ which has a K\"ahler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the K\"ahler form is exact on the minimal…
New examples of extremal K\"ahler metrics on blow-ups of parabolic ruled surfaces are constructed. The method is based on the gluing construction of Arezzo, Pacard and Singer. This enables to endow ruled surfaces of the form…
We prove the expansion formula for the classical Futaki invariants on the blowup of K\"ahler surfaces, which explains the balancing condition of Arezzo-Pacard. The relation with Stoppa's result is also discussed.
We show that at generic points blow-ups/tangents of differentiability spaces are still differentiability spaces; this implies that an analytic condition introduced by Keith as an inequality (and later proved to actually be an equality)…
Ancient solutions arise in the study of parabolic blow-ups. If we can categorize ancient solutions, we can better understand blow-up limits. Based on an argument of Giga and Kohn, we give a Liouville-type theorem restricting ancient,…
We prove finite-time Type-I blowup for the three-dimensional incompressible Euler equations in the axisymmetric no-swirl class, with initial velocity in $C^{1,\alpha}(\mathbb{R}^3)\cap L^2(\mathbb{R}^3)$, odd symmetry in $z$, and…
We study twisted cohomologies with paracompactifying families of supports. The Kunneth theorems, Leray-Hirsch theorems and self-intersection formulae are established. Based on these results, we eventually give explicit expressions of…