arXiv research

This paper studies a specific blow-up algorithm for sop polynomials and their RLCT.

Study on half spheres solves Nirenberg problem with complex blow-up analysis.

The paper defines and constructs almost complex blow-ups on 4D almost complex manifolds.

Formula derived for holomorphic Poisson blow-ups.

Study identifies numerical signs of blow-up in hydrodynamic equations.

Formula derived for Bott-Chern classes in complex blow-ups.

Explains blow-ups for Lie groupoids and algebroids, comparing different methods.

The paper derives a formula for Chow weights of toric blow-ups.

Study on curvature blow-up rates in black hole interiors from gravitational collapse.

The paper examines the blow-up of Ricci curvatures in conformal metrics.

We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a b…

We study blow-ups in generalized complex geometry. To that end we introduce the concept of holomorphic ideal, which allows one to define a blow-up in the category of smooth manifolds. We then investigate which generalized complex submanifolds are suitable for blowing up. Two classes naturally appear; generalized Poisso…

The paper analyzes high-dimensional sphere solutions to the Nirenberg problem with residual mass.

The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up …

The Yamabe flow can blow up in infinite time with small perturbations.

In this paper, we study the blow-up of a locally conformal symplectic manifold.We show that there exists a locally conformal symplectic structure on the blow-up of a locally conformal symplectic manifold along a compact induced symplectic submanifold.

Study on spinor field equation on spheres, focusing on blow-up analysis.

Two approaches study the homotopy of blow ups in algebraic and symplectic geometry.

Study on blow-up behavior of sign-changing solutions for Yamabe equation.

Proves inextendibility of weak null singularities from curvature blow-up.

Desingularizes singular foliations with a locally compact groupoid.

Corrected Monti's blow-up analysis for H-minimizing sets in Heisenberg group.

The article proves conditions for blow-ups of lcK spaces to remain lcK.

Finite-time blow-up in Yang-Mills flow for small energy initial connections.

The aim of this article is to study expansions of solutions to an extremal metric type equation on the blow-up of constant scalar curvature Kähler surfaces. This is related to finding constant scalar curvature Kähler (cscK) metrics on K-stable blow-ups of extremal Kähler surfaces

Study shows continuity and geometric regularity of Kähler-Ricci flow blow-up limits.

We derive a blow-up formula for the de Rham cohomology of a local system of complex vector spaces on a compact complex manifold. As an application, we obtain the blow-up invariance of $E_{1}$-degeneracy of the Hodge-de Rham spectral sequence associated to a local system of complex vector spaces.

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) passes to tangents. As an application, we characterize the $p$-weak gradient on iter…

We continue the study of blow-ups in generalized complex geometry with the blow-up theory for generalized Kähler manifolds. The natural candidates for submanifolds to be blown-up are those which are generalized Poisson for one of the two generalized complex structures and can be blown up in a generalized complex manner…

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single stand…

CR structure on S³ with non-compact solutions to CR Yamabe problem.

Study on curvature blow-up and convergence of continuity method on Hirzebruch surface.

We study blow-ups around fixed points at Type I singularities of the Ricci flow on closed manifolds using Perelman's W-functional. First, we give an alternative proof of the result obtained by Naber and Enders-Müller-Topping that blow-up limits are non-flat gradient shrinking Ricci solitons. Our second and main result …

In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along…

We prove some related results concerning blow-up solutions for the Jang equation. First: it has been shown that, given an outermost marginally outer trapped surface (MOTS) Σ, there exists a solution to Jang's equation which blows up at Σ. Here we show that in addition, large classes of spherically symmetric initial dat…

Study uses blow-up method to solve PMC problems with fixed boundaries.

Inspired by the recent works of S. Rao--S. Yang--X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse--Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse--Novikov cohomology by introducing the relative Morse--Novikov cohomology group via sheaf cohomology theory and pr…

New examples of extremal Kähler 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 $\mathbb{P}(\mathcal{O}\oplus L)$ with special parabolic structures such that the associated iter…

Many examples of nonpositively curved closed manifolds arise as blow-ups of projective hyperplane arrangements. If the hyperplane arrangement is associated to a finite reflection group W, and the blow-up locus is W-invariant, then the resulting manifold M will admit a cell decomposition whose maximal cells are all comb…

We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples associated to the vanishing theorems of Girbau, Kawamata-Viehweg and Green-Lazar…

In this paper we study the behaviour of the Lefschetz property under the blow-up construction. We show that it is possible to reduce the dimension of the kernel of the Lefschetz map if we blow up along a suitable submanifold satisfying the Lefschetz property. We use that, together with results about Massey products, to…

We generalize Fulton and MacPherson's configuration space construction to weighted filtered manifolds.

Solve supercritical Yamabe problem on manifolds with non-umbilic boundary.

Solutions grow for a special type of math problem on curved spaces.

We prove a gluing formula for Seiberg--Witten invariants which describes in particular the behaviour of the invariant under blow-up and rational blow-down.

Level set flow's singularities are type I under 2-convexity, leading to specific curvature blow-up rates.

In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds are characterised by the blow up of the mean curvature.

Study symplectic forms on manifolds to find Lagrangian pinwheels that can be separated.