arXiv research

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

Study real semi-stable degenerations and describe real loci via blow-ups.

In each dimension $N\geq 3$ and for each real number $λ\geq 1$, we construct a family of complete rotationally symmetric solutions to Ricci flow on $\mathbb{R}^{N}$ which encounter a global singularity at a finite time $T$. The singularity forms arbitrarily slowly with the curvature blowing up arbitrarily fast at the r…

Kontsevich's classes distinguish smooth structures on fiber bundles.

Study of separatrix configurations in holomorphic flows with real time.

Extends BCOV invariant to pairs of Calabi-Yau manifolds and pluricanonical divisors.

Real blow-up, including inhomogeneous versions, of boundary faces of a manifold (with corners) is an important tool for resolving singularities, degeneracies and competing notions of homogeneity. These constructions are shown to be particular cases of `generalized boundary blow-up' in which a new manifold and blow-down…

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.

We prove that the half-integer valued local index of an isolated umbilic point on a $C^{3+α}$-smooth convex surface in Euclidean 3-space is less than two. The approach is to study the co-kernel of an associated Riemann-Hilbert boundary value problem. The link between the local and global is a semi-local technique that …

Formula derived for holomorphic Poisson blow-ups.

Study bigraded formality and Aeppli-Bott-Chern-Massey products on complex manifolds.

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.

We prove that for every compact, connected, differentiable 3--manifold $M$ there is a compact complex manifold $X$ which can be obtained from projective 3--space by a sequence of smooth, real blow ups and downs such that $M$ is diffeomorphic to the set of real points of $X$. By earlier results, such an $X$ can almost n…

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

A steady state (or equilibrium point) of a dynamical system is hyperbolic if the Jacobian at the steady state has no eigenvalues with zero real parts. In this case, the linearized system does qualitatively capture the dynamics in a small neighborhood of the hyperbolic steady state. However, one is often forced to consi…

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.

Constructing manifold bundles from orbifolds and proving the existence of free subgroups in second homotopy groups.

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 topology of the orbit space, $Y$, for the action of the complex conjugation on a complex surface, $X$, defined over reals, is studied. I give a criterion for blow-up stable triviality of $Y$ (which implies vanishing of its Seiberg-Witten invariants). The main result concerns the double planes branched along the com…

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 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 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 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 of curvature blow-up in noncompact hypersurfaces using mean curvature flow.

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…