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我來轉慶傑和田剛的澄清說明
送交者: sgy 2005年10月13日21:18:05 於 [教育學術] 發送悄悄話

在丘成桐指責田剛抄襲(自然也指慶傑抄襲了)之後,慶傑和田剛已經在
他們文章中作了澄清。看了一下這些澄清以及兩個版本的文章,感覺
沒有抄襲或剽竊。第一個version中,的確有"main challenge"這
樣的說法,但這和抄襲無關。即使給credit時沒有給得讓丘成桐舒服,
也是一個溝通問題,就像洪家興和丘成桐關於那本書的署名問題一樣,
完全可以以正常的溝通來解決。

數學界的規矩通常是:一旦有人明確將一個問題作為open problem
或open question提出,人人都可以去做,誰先寫出文章的誰拿credit。
所以,即使不是內行,也可以看出所謂的抄襲指控是不成立的。
如果成立,從此以後沒有人敢做任何人提出的open problem或open
question了。

下面是慶傑和田剛所專門澄清這一個事實的三個註:

1. After we posted our first version of this paper, we got
some feedbacks indirectly about our main result compared to
previous results on this topic. In this new version we
stated our main result more precisely and gave more specific
references for a clearer comparison of our main result
to the previous ones.

2. The uniqueness problem addressed here was referred as the
global uniqueness of stable CHC surfaces in [HY]. Their
result on this global uniqueness was stated in Theorem 5.1
in [HY]. They proved that for q > 1/2 , if H sufficiently
small, there is a unique stable constant mean curvature
surface of mean curvature H outside BH^{−q}(0). It has been
a long-standing question whether stable constant mean
curvature surfaces are unique outside a fixed compact subset.
In the paragraph after Theorem 5.1 on page 301, Huisken and
Yau stated: “it is an open question whether stable
constant mean curvature surfaces are actually completely
unique outside a fixed compact subset.” Our main theoerm
gives an affirmative answer to this question.

3. In [HY], a global estimate was sought after (cf. Lemma 5.6
in [HY]), with a compromise to assume that the inner radius
is not smaller than H^{−q} for q > 1/2 . They stated in the
paragraph after Theorem 5.1 (page 21, [HY]) that their
assumption on inner radius “seems to be optimal from
a technical point of view”. While in this paper we do
different estimates in three different scales.
Particularly we establish some decay estimate for the
intermediate scales by using an asymptotic
analysis developed in [QT].

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