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- W3095142482 abstract "We show the analogy of Cauchy's surface area formula for the Heisenberg groups $mathbb{H}_n$ for $ngeq 1$, which states that the p-area of any compact hypersurface $Sigma$ in $mathbb{H}_n$ with its p-normal vector defined almost everywhere on $Sigma$ is the average of its projected p-areas onto the orthogonal complements of all p-normal vectors of the Pansu spheres (up to a constant). The formula provides a geometric interpretation of the p-areas defined by Cheng-Hwang-Malchiodi-Yang [9] in $mathbb{H}_1$ and Cheng-Hwang-Yang [7] in $mathbb{H}_n$ for $ngeq 2$. We also characterize the projected areas for rotationally symmetric domains in $mathbb{H}_n$, namely, for any rotationally symmetric domain with boundary in $mathbb{H}_n$, its projected p-area onto the orthogonal complement of any normal vector of the Pansu spheres is a constant, independent of the choices of the projected directions." @default.
- W3095142482 created "2020-11-09" @default.
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- W3095142482 date "2020-10-27" @default.
- W3095142482 modified "2023-09-27" @default.
- W3095142482 title "Cauchy surface area formula in the Heisenberg groups" @default.
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