arXiv subjects

Anuk Dayaprema

Publications and source records attributed to Anuk Dayaprema.

4 recordsLinked to original sources

arXiv2026

The semilinear heat inequality with Morrey initial data on Riemannian manifolds

The goal of this paper is to obtain estimates for nonnegative solutions of the differential inequality $$\left(\frac{\partial}{\partial t} - Δ\right) u \leq A u^p + B u $$ with small initial data in borderline Morrey norms over a Riemannian manifold with bounded geometry. We obtain $L^\infty$ estimates assuming $$\|u(\cdot,0)\|_{M^{q, \frac{2q}{p-1}}} + \sup_{0 \leq t < T} \|u(\cdot, t) \|_{L^s} < δ,$$ where $1 < q \leq q_c := \frac{n(p-1)}{2}$ and $1 \leq s \leq q_c$. Assuming also a bound on $\|u(\cdot, 0)\|_{M^{q', λ'}}$, where $\frac{λ'}{2q'} < \frac{1}{p-1}$, we get an improved estimate near the initial time. These results have applications to geometric flows in higher dimensions.

math.AP↗

arXiv2026

Convergence of the Yang-Mills flow on ALE gravitational instantons

We prove a sharp convergence theorem for the Yang-Mills flow on an $\mathrm{S}\mathrm{U}(r)$-bundle over a locally hyperKähler ALE 4-manifold. Our main result is a noncompact version of the "parabolic gap theorem" previously established by the authors.

math.DG↗

arXiv2026

Parabolic gap theorems for the Yang-Mills energy

We prove parabolic versions of several known gap theorems in classical Yang-Mills theory. On an $\mathrm{SU}(r)$-bundle of charge $κ$ over the 4-sphere, we show that the space of all connections with Yang-Mills energy less than $4 π^2 \left( |κ| + 2 \right)$ deformation-retracts under Yang-Mills flow onto the space of instantons, allowing us to simplify the proof of Taubes's path-connectedness theorem. On a compact quaternion-Kähler manifold with positive scalar curvature, we prove that the space of pseudo-holomorphic connections whose $\mathfrak{sp}(1)$ curvature component has small Morrey norm deformation-retracts under Yang-Mills flow onto the space of instantons. On a nontrivial bundle over a compact manifold of general dimension, we prove that the infimum of the scale-invariant Morrey norm of curvature is positive.

math.DG↗

arXiv2022

Construction of Nahm data and BPS monopoles with continuous symmetries

We study solutions to Nahm's equations with continuous symmetries and, under certain (mild) hypotheses, we classify the corresponding Ansätze. Using our classification, we construct novel Nahm data, and prescribe methods for generating further solutions. Finally, we use these results to construct new BPS monopoles with spherical symmetry.

math-ph↗