We prove solution uniqueness for the genus one Canham variational problem arising in the shape prediction of biomembranes. The proof builds on a result of Yu and Chen that reduces the variational problem to proving non-negativity of a sequence defined by a linear recurrence relation with polynomial coefficients. We combine rigorous numeric analytic continuation of D-finite functions with classic bounds from singularity analysis to derive an effective index where the asymptotic behaviour of the sequence, which is positive, dominates the sequence behaviour. Positivity of the finite number of remaining terms is then checked computationally.

中文翻译：

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通过数值分析延续的序列正性：生物膜 Canham 模型的独特性

我们证明了生物膜形状预测中出现的一类 Canham 变分问题的解唯一性。该证明建立在 Yu 和 Chen 的结果之上，该结果将变分问题简化为证明由具有多项式系数的线性递推关系定义的序列的非负性。我们将 D 有限函数的严格数值解析延拓与奇点分析的经典边界相结合，得出一个有效指标，其中序列的渐近行为是正的，主导序列行为。然后通过计算检查剩余项的有限数量的正性。