In a convex manner; in the direction of or with the quality of being convex.
Convex (Latin convexus) + -ly (adverbial suffix). The standard adverbial form of the adjective convex, following regular English adverbial morphology.
You won't find 'convexly' in most dictionaries or everyday speech, but it's absolutely standard English construction. It's a word that exists grammatically but is almost never needed because we rarely describe actions or states 'in a convex way.'
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