Question

Would you mind my coming with you mind后面为什么用my而不用me

Answer 1

mind 后加doing ,my 作doing 的逻辑主语,和mind没关系
参考：
ing分词也可以有自己的逻辑主语,即由-ing分词短语的一部分表示,这种带有逻辑主语的-ing分词短语叫做ing分词复合结构,它包括三种情况：
A.用名词或人称代词的所有格形式,在非正式文体中用名词的原形或人称代词的宾格形式表示-ing分词的逻辑主语,这种逻辑主语的-ing分词复合结构通常起名词的作用,在句中作主语,宾语,表语和同位语.例如：
作主语
Their accepting the money will be considered.他们接受钱的事将会被考虑到.
作宾语
I can't tolerate his constant complaining about everything.我们不能容忍他经常抱怨每件事.
作表语
What her husband insisted on is her cleaning the house every day.她丈夫坚持让她每天打扫房子.
作同位语
He has devoted his life to one cause,fighting against all political and social in justice.他已经把他的生命献身于一个事业,反对所有政治和社会的不公平.
名词的原形比所有格更常用,在It's no use/good这个结构中只能用名词的原形,代词的属格形式比宾格形式更常用,作主语时只能用属格形.例如：
It's no use your telling me not to worry.你告诉我不要担心,但没用.
It's no use your father telling me not to worry.你父亲告诉我不要担心,但没用.
不定代词,指示代词和没有或不易构成属格形式的名词及其短语通常都用原形.例如：
I object to anybody smoking in my room.我反对任何人在我房间吸烟.
I didn't notice the door being shut.我没有注意到门被关了.
He laughed at my brother and me liking rice pudding.他嘲笑我弟弟和我喜欢布丁.
B.用名词的原形或代词的主格形式作ing分词的逻辑主语,这种ing分词复合结构又叫做ing分词独立结构.例如：
It being Sunday,the stores were not open.星期天商店没开门.(此句中表示时间的逻辑主语it可以省去)
Christmas Day being a holiday,the shops were all closed.圣诞节假期商店都关门了.
They had many talks with the native,the guide acting as interpreter.他们已经同土著人谈过几次,向导充当的翻译.
C.表示存在的there be结构的ing分词复合结构通常用作宾语和状语,逻辑主语there直接放在ing分词之前.例如：
No one would have dreamed of there being such a place.没有人梦想过有如此的地方.
There having been some matters about the bookkeeper's honesty,the company
asked him to resign.由于一些关于图书管理员的诚实问题,公司叫他辞职.