M. Stolarski

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20192026

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math.DG2026

Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics

Maxwell Stolarski, Wei-Bo Su

For each integer $K \geq 2$ when $n \geq 4$ , and for $K = 2, 3, 4$ when $n = 3$ , we construct an almost-calibrated Lagrangian mean curvature flow $L_{K} (t)$ in $C^{n}$ , starting from…

math.DG2026

Spectral Analysis for Finite-Time Singularities of Lagrangian Mean Curvature Flow

Maxwell Stolarski, Wei-Bo Su

Let $C$ be a $G$ -invariant special Lagrangian cone admitting a scaled family of $G$ -invariant special Lagrangian desingularizations $a L$ which converge to $\mat…

math.DG2026

Integrable Deformations and Stability of the Ricci Flow

Maxwell Stolarski, Alex Waldron

We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the…

math.DG2023

On the Structure of Singularities of Weak Mean Curvature Flows with Mean Curvature Bounds

Maxwell Stolarski

This paper studies singularities of mean curvature flows with integral mean curvature bounds $H \in L^{\infty} L_{l oc}^{p}$ for some $p \in (n, \infty]$ . For such flows, any tangent f…

math.DG2020

Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature

Maxwell Stolarski

In [Vel94], Velazquez constructed a countable collection of mean curvature flow solutions in $R^{N}$ in every dimension $N \geq 8$ . Each of these solutions becomes singular i…

math.DG2019

Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow

Maxwell Stolarski

For any manifold $N^{p}$ admitting an Einstein metric with positive Einstein constant, we study the behavior of the Ricci flow on high-dimensional products $M = N^{p} \times S^{q + 1}$ w…