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Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
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Can this integral be made nonpositive?
Let $M^2 \subset \mathbb{S}^3$ be a closed and orientable embedded (and minimal, if important) surface. Choose a unit normal vector field $\eta: M \to \mathbb{S}^3$ along $M$ and a point $p_0 \in \mat …
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How does one interpret the wetting area?
This may be a simple question, but I decided to post it here (not just on MSE) because it is very related to a research topic: capillary surfaces.
Let $(M^3,g)$ be a Riemannian $3$-manifold with bound …