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Results tagged with geometric-measure-theory
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user 124749
Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.
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Lebesgue dominated convergence for currents
I am learning current theory presently. In Chap 3.3-Definition of Monge-Ampère Operators, J.-P. Demailly, Complex analytic and differential geometry, I am a little confused as follows.
Let $X$ be a …
- 391
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Are positivity for forms and that for currents consistent when talking about smooth forms?
Let $X$ be a complex manifold and $\theta$ a smooth $(1,1)$-form on $X$.
(1) If $\theta>0$ in the sense of currents, then can we deduce that $\theta>0$ in the sense of forms?
(2) If $\theta>0$ in the …
- 391
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About the current of finite mass
In Demailly's e-book Complex analytic and differential geometry,
chap3-(1.14) Proposition is stated as follows:
Every positive current $T=i^{(n-p)^{2}} \sum T_{I, J} d z_{I} \wedge d \bar{z}_{J}$ i …
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