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arXiv · 2605.24317

Quantitative Stability of Generalized $p$-Area Minimizing Surfaces

Amir Moradifam·Gerardo Orozco-Fernandez
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Abstract

We study the stability of $p$-area minimizing surfaces in the Heisenberg group under perturbations of the weight function and the drift vector field in generalized least gradient problems of the form \[ \inf_{w\in BV_0(\Omega)} \int_\Omega \left(a(x)|Dw+F(x)|+H(x)w\right)\,dx. \] Owing to the lack of strict convexity, establishing stability of minimizers is challenging. We derive quantitative stability estimates for minimizers. In particular, under suitable nondegeneracy and geometric assumptions, we obtain $L^1$ and $W^{1,1}$ stability estimates with respect to perturbations of the weight function $a$ and the drift vector field $F$. We further establish unified quantitative stability estimates under simultaneous perturbations of all principal parameters, namely $a$, $F$, and $H$. Numerical simulations illustrating the stability theory are also presented.

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Amir Moradifam, Gerardo Orozco-Fernandez. 2026-05-23. Quantitative Stability of Generalized $p$-Area Minimizing Surfaces. https://arxiv.org/abs/2605.24317

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