MODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION
In this dissertation, we study several aspects of an D-dimensional submanifold ?D embedded in (D+1)-dimensional manifold MD+1, ?D ? MD+1 and the modified Geroch functional in D ? 2. We show that a submanifold ?D with vanishing mean curvature, H = 0, is a critical point of MGF using the first deri...
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| Format: | Dissertations |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/37825 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | In this dissertation, we study several aspects of an D-dimensional submanifold ?D
embedded in (D+1)-dimensional manifold MD+1, ?D ? MD+1 and the modified
Geroch functional in D ? 2. We show that a submanifold ?D with vanishing mean
curvature, H = 0, is a critical point of MGF using the first derivative formula. We
also prove that MGF is non-decreasing for t ? 0. This result is obtained by doing the
calculation of the first derivative of MGF. Furthermore, from the second derivative
of MGF, we obtain that MGF has a local minimum and maximum value. |
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