Related papers: Divisorial contractions in dimension three which c…
The spanning surface defect uses spanning surfaces of a knot in the $3$-sphere to measure how far a knot is from being alternating. We refine the spanning surface defect and extend the definition to take into account surfaces in the…
A commuting triple of Hilbert space operators $(A,B,P)$, for which the closed tetrablock $\bar{\mathbb E}$ is a spectral set, is called a \textit{tetrablock-contraction} or simply an $\mathbb E$-\textit{contraction}, where \[ \mathbb…
This is the second part of the series of papers on symmetry properties of a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of general form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. At first, we review…
In this paper we try to collect certain contractions which can be obtained by equivalent metric of cone metric.
In this paper we give a criterion for an isolated, hypersurface singularity of dimension $n\ (\geq 2)$ to have the canonical modification by means of a suitable weighted blow-up. Then we give a counter example to the following conjecture by…
The existence and uniqueness of canonical singular solutions of the J-equation and the deformed Hermitian Yang Mills (dHYM) equation was proved in \cite{DMS24} on compact K\"{a}hler surfaces. In this paper, we study the singularity…
We show that a sequence of smooth analytic subsets of dimension s of the unit ball of C^l, for which the curvature is bounded by the volume, converges to a lamination of dimension s in a weak sense.
We apply Vojta's conjecture to blowups and deduce a number of deep statements regarding (generalized) greatest common divisors on varieties, in particular on projective space and on abelian varieties. Special cases of these statements…
We study exceptional loci of F-blowups of normal toric varieties. In the $\Q$-factorial case, this study amounts to studying the exceptional loci of $G$-Hilbert schemes. We give a formula for the dimension of the center of a prime divisor…
Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of…
We show a new example of blow-up behaviour for the prescribed $Q$-curvature equation in even dimension $6$ and higher, namely given a sequence $(V_k)\subset C^0(\mathbb{R}^{2n})$ suitably converging we construct {for $n\geq 3$} a sequence…
A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and…
We study how different types of blow-ups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blow-ups can…
We study the local dimension of the convolution of two measures. We give conditions for bounding the local dimension of the convolution on the basis of the local dimension of one of them. Moreover, we give a formula for the local dimension…
We study the collapsibility of finite simplicial complexes of dimension 3 endowed with a CAT(0) metric. Our main result states that, under an additional hypothesis, finite simplicial 3-complexes endowed with a CAT(0) metric collapse to a…
Let X/T be a one parameter family of canonical 3-folds and let D be a Weil divisor on it flat over T. We study the problem of when the D_t-minimal models of X_t form a family and we obtain conditions for this to happen. As an application of…
We consider equivariant wave maps from $\mathbb{R}^{d+1}$ to $\mathbb{S}^d$ in supercritical dimensions $3\leq d\leq 6$. Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. The gradient of solutions may blow up as $\varepsilon$, the distance between inclusions, approaches to $0$. An upper bound for the…
We prove a universal property for blow-ups in regularly immersed subschemes, based on a notion we call "virtual effective Cartier divisor". We also construct blow-ups of quasi-smooth closed immersions in derived algebraic geometry.
For the prescribed scalar curvature equation on $S^n$ ($n \ge 6$), we consider the situation where the number of bubbles tends to infinity in the Lyapunov-Schmidt (finite dimension) reduction method. In an outstanding paper by Wei and Yan,…