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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id-itb.:378252019-04-24T09:47:10ZMODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION Radjabaycolle, Flinn Fisika Indonesia Dissertations modified functional Geroch, submanifold, critical point, monotonicity INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/37825 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. text |
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Indonesia Indonesia |
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Fisika |
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Fisika Radjabaycolle, Flinn MODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION |
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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. |
| format |
Dissertations |
| author |
Radjabaycolle, Flinn |
| author_facet |
Radjabaycolle, Flinn |
| author_sort |
Radjabaycolle, Flinn |
| title |
MODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION |
| title_short |
MODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION |
| title_full |
MODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION |
| title_fullStr |
MODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION |
| title_full_unstemmed |
MODIFIED GEROCH FUNCTIONAL IN HIGHER DIMENSION |
| title_sort |
modified geroch functional in higher dimension |
| url |
https://digilib.itb.ac.id/gdl/view/37825 |
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1822924915831996416 |