Abstract
In this work,
we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in
Funding source: Independent Research Fund Denmark
Award Identifier / Grant number: DFF Sapere Aude 7027-00110B
Funding source: Danish National Research Foundation
Award Identifier / Grant number: CPH-GEOTOP-DNRF151
Funding source: Carlsberg Foundation
Award Identifier / Grant number: CF21-0680
Funding statement: The authors were partially supported by DFF Sapere Aude 7027-00110B, by CPH-GEOTOP-DNRF151 and by CF21-0680 from respectively the Independent Research Fund Denmark, the Danish National Research Foundation and the Carlsberg Foundation.
A The sequence
(
E
n
)
In this appendix, we show the following lemma.
Lemma A.1.
The sequence
Proof.
It is proved in [38, A.4 Lemma] that the entropy of the n-sphere
and the sequence
From (3.1) and (A.2) we obtain
where
Direct calculations give
and
Using (A.4), (A.3) and (A.6), one obtains (A.1).
Next we show
Thus
Together with
Since
The inequality implies
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