What is the meaning of -mark in the name Denmark and is it in any way comparable to -mark in Hitler's name Ostmark for Austria?

The suffix -mark is believed to mean woodland or borderland.

"Most handbooks derive the first part of the word, and the name of the people, from a word meaning "flat land", related to German Tenne "threshing floor", English den "cave", Sanskrit dhánuṣ- "desert". The -mark is believed to mean woodland or borderland, with probable references to the border forests in south Schleswig, maybe similar to Finnmark, Telemark or Dithmarschen."
https://en.wikipedia.org/wiki/Denmark#Etymology

It does seem to be comparable to the renaming of Austria to "Ostmark" in the sense that the suffix "-mark" means borderland or frontier, as in the "eastern border" when Austria was annexed into Nazi Germany in 1938 during the Anschluss period.
http://aeiou.iicm.tugraz.at/aeiou.encyclop.o/o657342.htm;internal&action=_setlanguage.action?LANGUAGE=en
https://en.wikipedia.org/wiki/Ostmark
https://en.wikipedia.org/wiki/Anschluss

The word is related to English "Marches".

https://en.wikipedia.org/wiki/Marches

Now, that's really interesting, author. Maybe we should paste in some of that stuff from your reference.

The Frankish word marka and the Old English word mearc both come from Proto-Germanic *marko, which itself comes from the Proto-Indo-European root *mereg-, meaning "edge, boundary". The root *mereg- gave Armenian marz ("border, land"), Latin margo ("margin"), Old Irish mruig ("borderland"), Persian marz ("border, land") and Norse merki ("boundary, sign") and mörk ("borderland, forest"). It seems in Old English "mark" meant "boundary", or "sign of a boundary", and the meaning later evolved into "sign in general", "impression or trace forming a sign". The word "march" in the sense of borderland was borrowed from French marche, which had borrowed it from Frankish. The word "mark" in the sense of borderland is a modern borrowing from German Mark, though in some cases it is simply short for Markgrafschaft.

In Danish (and Norwegian) "mark" today mainly means "field" or "ground". Many places in Denmark are named, for example Østermark, which means the Eastern Field.

You find the same meaning in the name of the Italian province "Marche".

https://en.wikipedia.org/wiki/Marche

Marches also means borderland, not just field or ground. You find "marches" all over Europe, and in this site you can find out where.

https://en.wikipedia.org/wiki/Marches

The name of the English region Mercia comes from boundary but now it forms the English midlands.

https://en.wikipedia.org/wiki/Mercia

"Mercia was one of the kingdoms of the Anglo-Saxon Heptarchy. It was centred on the valley of the River Trent and its tributaries in the region now known as the English Midlands. The name is a Latinisation of the Old English Mierce, meaning "border people".

Mercia's exact evolution from the Anglo-Saxon invasions is more obscure than that of Northumbria, Kent, or even Wessex. Archaeological surveys show that Angles settled the lands north of the River Thames by the sixth century. The name Mercia is Old English for "boundary folk" (see marches), and the traditional interpretation was that the kingdom originated along the frontier between the Welsh and the Anglo-Saxon invaders, although P. Hunter Blair has argued an alternative interpretation that they emerged along the frontier between the kingdom of Northumbria and the inhabitants of the Trent river valley."

[Added reference - McG]