Does Windows Phone 7 support HTML5 browser?
No, not yet. You will have to wait for the update at the end of the year , which will lead IE9 to Windows Phone 7.
The current WP7 browser is somewhere between IE7 and IE9.
The WP7 update has just been updated, I assume that IE9 (and multitasking) will not appear until the end of this year.
WP7 comes with a hybrid of IE7 and IE8, which implies the lack of HTML5 functionality. IE9, which will be released after a while, will support HTML5.
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