# Geometric Analysis Reference Question: \$ C ^ 1 \$ Estimate for a stable minimum surface

I am looking for an answer to the following question: Let $$(M, g)$$ be a complete Riemannian manifold and $$Sigma subset M$$ a closed, stable minimal surface. Can you prove? $$C ^ 1$$ Estimates for $$Sigma$$ that depends only on $$C ^ 0$$Data of the metric tensor? Does the situation change when you replace stability with area minimization?

I can find several resources that deal with higher-order (curvature) estimates, which are usually more dependent $$g$$ (at least $$C ^ 1$$) however.